Encyclopedia of optimization

Cover Page......Page 1
Encyclopedia of Optimization......Page 2
Preface to the Second Edition......Page 5
About the Editors......Page 6
Editorial Board Members......Page 8
List of Contributors......Page 10
ABS Algorithms for Linear Equations and Linear Least Squares......Page 33
ABS Algorithms for Optimization......Page 39
Adaptive Convexification in Semi-Infinite Optimization......Page 46
Adaptive Global Search......Page 51
Adaptive Simulated Annealing and its Application to Protein Folding......Page 53
Airline Optimization......Page 58
Algorithmic Improvements Using a Heuristic Parameter, Reject Index for Interval Optimization......Page 62
Algorithms for Genomic Analysis......Page 65
Alignment Problem......Page 86
αBB Algorithm......Page 93
Alternative Set Theory......Page 105
Approximation of Extremum Problems with Probability Functionals......Page 110
Approximation ofMultivariate Probability Integrals......Page 115
Approximations to Robust Conic Optimization Problems......Page 122
Archimedes and the Foundations of Industrial Engineering......Page 128
Asset Liability Management Decision Support System......Page 130
Assignment and Matching......Page 138
Assignment Methods in Clustering......Page 140
Asymptotic Properties of Random Multidimensional Assignment Problem......Page 146
Asynchronous Distributed Optimization Algorithms......Page 155
Auction Algorithms......Page 160
Automatic Differentiation: Calculation of the Hessian......Page 165
Automatic Differentiation: Calculation of Newton Steps......Page 169
Automatic Differentiation: Geometry of Satellites and Tracking Stations......Page 174
Automatic Differentiation: Introduction, History and Rounding Error Estimation......Page 185
Automatic Differentiation: Parallel Computation......Page 191
Automatic Differentiation: Point and Interval......Page 197
Automatic Differentiation: Point and Interval Taylor Operators......Page 203
Automatic Differentiation: Root Problemand Branch Problem......Page 208
Bayesian Global Optimization......Page 214
Bayesian Networks......Page 218
Beam Selection in Radiotherapy Treatment Design......Page 227
Best Approximation in Ordered Normed Linear Spaces......Page 233
Bilevel Fractional Programming......Page 250
Bilevel Linear Programming......Page 252
Bilevel Linear Programming: Complexity, Equivalence to Minmax, Concave Programs......Page 256
Bilevel Optimization: Feasibility Test and Flexibility Index......Page 259
Bilevel Programming......Page 270
Bilevel Programming: Applications......Page 272
Bilevel Programming: Applications in Engineering......Page 274
Bilevel Programming Framework for Enterprise-Wide Process Networks Under Uncertainty......Page 279
Bilevel Programming: Global Optimization......Page 286
Bilevel Programming: Implicit Function Approach......Page 291
Bilevel Programming: Introduction, History and Overview......Page 297
Bilevel Programming in Management......Page 300
Bilevel Programming: Optimality Conditions and Duality......Page 305
Bilinear Programming......Page 310
Bilinear Programming: Applications in the Supply Chain Management......Page 313
Bi-Objective Assignment Problem......Page 319
Biquadratic Assignment Problem......Page 324
Bisection Global Optimization Methods......Page 325
Boolean and Fuzzy Relations......Page 328
Bottleneck Steiner Tree Problems......Page 342
Boundary Condition Iteration BCI......Page 344
Bounding Derivative Ranges......Page 349
Bounds and Solution Vector Estimates for Parametric NLPS......Page 356
Branch and Price: Integer Programming with Column Generation......Page 359
Branchwidth and Branch Decompositions1......Page 363
Broadcast Scheduling Problem......Page 370
Broyden Family ofMethods and the BFGS Update......Page 376
CapacitatedMinimum Spanning Trees......Page 378
Carathéodory, Constantine......Page 388
Carathéodory Theorem......Page 389
Checklist Paradigm Semantics for Fuzzy Logics......Page 390
Chemical Process Planning......Page 400
Cholesky Factorization......Page 405
CombinatorialMatrix Analysis......Page 408
Combinatorial Optimization Algorithms in Resource Allocation Problems......Page 413
Combinatorial Optimization Games......Page 418
Combinatorial Test Problems and Problem Generators......Page 422
Communication Network Assignment Problem......Page 425
Competitive Facility Location......Page 427
Competitive Ratio for Portfolio Management......Page 432
Complementarity Algorithms in Pattern Recognition......Page 436
Complexity Classes in Optimization......Page 444
Complexity of Degeneracy......Page 450
Complexity of Gradients, Jacobians, and Hessians......Page 456
Complexity and Large-Scale Least Squares Problems......Page 466
Complexity Theory......Page 478
Complexity Theory: Quadratic Programming......Page 482
Composite Nonsmooth Optimization......Page 485
Computational Complexity Theory......Page 488
Concave Programming......Page 493
Conjugate-Gradient Methods......Page 497
ContactMap OverlapMaximization Problem, CMO......Page 502
Continuous Approximations to Subdifferentials......Page 506
Continuous Global Optimization: Applications......Page 513
Continuous Global Optimization: Models, Algorithms and Software......Page 517
Continuous Reformulations of Discrete-Continuous Optimization Problems......Page 524
Continuous Review Inventory Models: (Q, R) Policy......Page 532
Contraction-Mapping......Page 536
Control Vector Iteration CVI......Page 540
Convex Discrete Optimization......Page 544
Convex Envelopes in Optimization Problems......Page 581
Convexifiable Functions, Characterization of1......Page 582
Convex Max-Functions......Page 586
Convex-Simplex Algorithm......Page 589
Copositive Optimization......Page 592
Copositive Programming......Page 595
Cost Approximation Algorithms......Page 598
Credit Rating and OptimizationMethods......Page 609
Criss-Cross Pivoting Rules......Page 615
Cutting PlaneMethods for Global Optimization......Page 621
Cutting-Stock Problem......Page 625
Cyclic Coordinate Method......Page 626
Data Envelopment Analysis......Page 628
Data Mining......Page 631
D.C. Programming......Page 638
Decision Support Systems withMultiple Criteria......Page 643
Decomposition Algorithms for the Solution of Multistage Mean-Variance Optimization Problems......Page 650
Decomposition in Global Optimization......Page 658
Decomposition Principle of Linear Programming......Page 661
Decomposition Techniques forMILP: Lagrangian Relaxation......Page 663
De Novo Protein Design Using Flexible Templates......Page 669
De Novo Protein Design Using Rigid Templates......Page 674
Derivative-Free Methods for Non-smooth Optimization......Page 679
Derivatives of Markov Processes and Their Simulation......Page 686
Derivatives of Probability and Integral Functions: General Theory and Examples......Page 689
Derivatives of Probability Measures......Page 695
Design Optimization in Computational Fluid Dynamics......Page 697
Design of Robust Model-Based Controllers via Parametric Programming......Page 708
Determining the Optimal Number of Clusters......Page 718
Deterministic and Probabilistic OptimizationModels for Data Classification......Page 725
Differential Equations and Global Optimization......Page 733
Dini and Hadamard Derivatives in Optimization......Page 741
Directed Tree Networks......Page 747
Direct Global Optimization Algorithm......Page 756
Direct Search Luus–Jaakola Optimization Procedure......Page 766
Discontinuous Optimization......Page 770
Discretely Distributed Stochastic Programs: Descent Directions and Efficient Points......Page 775
Discrete Stochastic Optimization......Page 782
Disease Diagnosis: Optimization-BasedMethods......Page 784
Disjunctive Programming......Page 815
Distance Dependent Protein Force Field via Linear Optimization......Page 818
Domination Analysis in Combinatorial Optimization......Page 823
Duality Gaps in Nonconvex Optimization......Page 833
Duality in Optimal Control with First Order Differential Equations......Page 836
Duality for Semidefinite Programming......Page 842
Duality Theory: Biduality in Nonconvex Optimization......Page 845
Duality Theory: Monoduality in Convex Optimization......Page 849
Duality Theory: Triduality in Global Optimization......Page 853
Dykstra’s Algorithm and Robust Stopping Criteria......Page 859
Dynamic Programming: Average Cost Per Stage Problems......Page 864
Dynamic Programming in Clustering......Page 868
Dynamic Programming: Continuous-time Optimal Control......Page 875
Dynamic Programming: Discounted Problems......Page 877
Dynamic Programming: Infinite Horizon Problems, Overview......Page 881
Dynamic Programming: Inventory Control......Page 884
Dynamic Programming and Newton’sMethod in Unconstrained Optimal Control......Page 887
Dynamic Programming: Optimal Control Applications......Page 893
Dynamic Programming: Stochastic Shortest Path Problems......Page 900
Dynamic Programming: Undiscounted Problems......Page 904
Dynamic Traffic Networks......Page 907
Economic Lot-Sizing Problem......Page 914
Eigenvalue Enclosures for Ordinary Differential Equations......Page 918
Ellipsoid Method......Page 921
Emergency Evacuation, OptimizationModeling......Page 931
Entropy Optimization: Interior PointMethods......Page 938
Entropy Optimization: Parameter Estimation......Page 943
Entropy Optimization: ShannonMeasure of Entropy and its Properties......Page 947
Equality-Constrained Nonlinear Programming: KKT Necessary Optimality Conditions......Page 952
Equilibrium Networks......Page 954
Equivalence Between Nonlinear Complementarity Problem and Fixed Point Problem......Page 958
Estimating Data for Multicriteria Decision Making Problems: Optimization Techniques......Page 962
Evacuation Networks......Page 971
Evolutionary Algorithms in Combinatorial Optimization......Page 981
Extended Cutting Plane Algorithm......Page 990
Extension of the Fundamental Theorem of Linear Programming......Page 997
Extremum Problems with Probability Functions: Kernel Type Solution Methods......Page 1000
Facilities Layout Problems......Page 1005
Facility Location with Externalities......Page 1009
Facility Location Problems with Spatial Interaction......Page 1012
Facility Location with Staircase Costs......Page 1019
Farkas Lemma......Page 1025
Farkas Lemma: Generalizations......Page 1028
Feasible Sequential Quadratic Programming......Page 1031
Feedback Set Problems......Page 1035
Fejér Monotonicity in Convex Optimization......Page 1046
Financial Applications of Multicriteria Analysis......Page 1054
Financial Equilibrium......Page 1065
Financial Optimization......Page 1070
Finite Complete Systems of Many-valued Logic Algebras......Page 1078
First Order Constraint Qualifications......Page 1085
Flow Shop Scheduling Problem......Page 1090
Forecasting......Page 1098
Fourier–Motzkin Elimination Method......Page 1104
Fractional Combinatorial Optimization......Page 1107
Fractional Programming......Page 1110
Fractional Zero-One Programming......Page 1121
Frank–Wolfe Algorithm......Page 1124
Frequency Assignment Problem......Page 1127
Fundamental Theorem of Algebra......Page 1131
FuzzyMulti-objective Linear Programming......Page 1133
Gasoline Blending and Distribution Scheduling: AnMILPModel......Page 1143
Gauss, Carl Friedrich......Page 1157
Gauss–Newton Method: Least Squares, Relation to Newton’s Method......Page 1159
Gene Clustering: A Novel Decomposition-Based Clustering Approach: Global Optimum Search with Enhanced Positioning......Page 1164
Generalizations of Interior Point Methods for the Linear Complementarity Problem......Page 1175
Generalized Assignment Problem......Page 1183
Generalized Benders Decomposition......Page 1192
Generalized Concavity in Multi-objective Optimization......Page 1205
Generalized Disjunctive Programming......Page 1210
Generalized Eigenvalue Proximal Support VectorMachine Problem......Page 1213
Generalized Geometric Programming: Mixed Continuous and Discrete Free Variables......Page 1215
Generalized Monotone MultivaluedMaps......Page 1223
Generalized Monotone Single Valued Maps......Page 1227
Generalized Monotonicity: Applications to Variational Inequalities and Equilibrium Problems......Page 1232
Generalized Networks......Page 1239
Generalized Nonlinear Complementarity Problem......Page 1244
Generalized Outer Approximation......Page 1245
Generalized Primal-relaxed Dual Approach......Page 1253
Generalized Semi-infinite Programming: Optimality Conditions......Page 1257
Generalized Total Least Squares......Page 1263
Generalized Variational Inequalities: A Brief Review......Page 1268
General Moment Optimization Problems......Page 1274
General Routing Problem......Page 1282
Genetic Algorithms......Page 1284
Genetic Algorithms for Protein Structure Prediction......Page 1287
Geometric Programming......Page 1290
Global Equilibrium Search......Page 1298
Globally Convergent Homotopy Methods......Page 1302
Global Optimization Algorithms for Financial Planning Problems......Page 1307
Global Optimization in the Analysis and Management of Environmental Systems......Page 1312
Global Optimization: Application to Phase Equilibrium Problems......Page 1316
Global Optimization Based on StatisticalModels......Page 1321
Global Optimization in Batch Design Under Uncertainty......Page 1324
Global Optimization in Binary Star Astronomy......Page 1329
Global Optimization: Cutting Angle Method......Page 1334
Global Optimization: Envelope Representation......Page 1341
Global Optimization: Filled Function Methods......Page 1346
Global Optimization: Functional Forms......Page 1353
Global Optimization: g- αBB Approach......Page 1358
Global Optimization in Generalized Geometric Programming......Page 1363
Global Optimization of Heat Exchanger Networks......Page 1367
Global Optimization: Hit and RunMethods......Page 1372
Global Optimization: Interval Analysis and Balanced Interval Arithmetic......Page 1376
Global Optimization in Lennard–Jones andMorse Clusters......Page 1380
Global Optimization in Location Problems......Page 1384
Global Optimization Methods for Harmonic Retrieval......Page 1389
Global Optimization Methods for Systems of Nonlinear Equations......Page 1394
Global Optimization in Multiplicative Programming......Page 1396
Global Optimization: p-αBB Approach......Page 1400
Global Optimization in Phase and Chemical Reaction Equilibrium......Page 1406
Global Optimization of Planar Multilayered Dielectric Structures......Page 1413
Global Optimization in Protein Folding......Page 1422
Global Optimization: Tight Convex Underestimators......Page 1441
Global Optimization Using Space Filling......Page 1448
Global Optimization in Weber’s Problem with Attraction and Repulsion......Page 1453
Pairwise Protein Sequence via Mixed-Integer Optimization......Page 1457
Global Supply Chain Models......Page 1464
Global Terrain Methods......Page 1467
Graph Coloring......Page 1474
Graph Planarization......Page 1478
Graph Realization via Semidefinite Programming......Page 1483
Greedy Randomized Adaptive Search Procedures......Page 1490
Gröbner Bases for Polynomial Equations......Page 1499
Hamilton–Jacobi–Bellman Equation......Page 1502
Hemivariational Inequalities: Applications inMechanics......Page 1506
Hemivariational Inequalities: Eigenvalue Problems......Page 1512
Hemivariational Inequalities: Static Problems......Page 1517
Heuristic and Metaheuristic Algorithms for the Traveling Salesman Problem......Page 1528
Heuristic Search......Page 1535
Heuristics for Maximum Clique and Independent Set......Page 1537
High-order Maximum Principle for Abnormal Extremals......Page 1549
High-order Necessary Conditions for Optimality for Abnormal Points......Page 1556
Hilbert’s Thirteenth Problem......Page 1564
History of Optimization......Page 1567
Homogeneous Selfdual Methods for Linear Programming......Page 1571
Hyperplane Arrangements......Page 1574
Hyperplane Arrangements in Optimization......Page 1576
IdentificationMethods for Reaction Kinetics and Transport......Page 1578
Ill-posed Variational Problems......Page 1585
Image Space Approach to Optimization......Page 1590
Implicit Lagrangian......Page 1596
Increasing and Convex-Along-Rays Functions on Topological Vector Spaces......Page 1600
Increasing and Positively Homogeneous Functions on Topological Vector Spaces......Page 1605
Inequality-constrained Nonlinear Optimization......Page 1615
Inference of Monotone Boolean Functions......Page 1620
Infinite Horizon Control and Dynamic Games......Page 1627
Information-based Complexity and Information-based Optimization......Page 1632
Integer Linear Complementary Problem......Page 1637
Integer Linear Programs for Routing and Protection Problems in Optical Networks......Page 1639
Integer Programming......Page 1646
Integer Programming: Algebraic Methods......Page 1653
Integer Programming: Branch and Bound Methods......Page 1663
Integer Programming: Branch and Cut Algorithms......Page 1672
Integer Programming: Cutting Plane Algorithms......Page 1679
Integer Programming Duality......Page 1686
Integer Programming: Lagrangian Relaxation......Page 1696
Integrated Planning and Scheduling......Page 1702
Interior PointMethods for Semidefinite Programming......Page 1708
Interval Analysis: Application to Chemical Engineering Design Problems......Page 1712
Interval Analysis: Differential Equations......Page 1715
Interval Analysis: Eigenvalue Bounds of Interval Matrices......Page 1718
Interval Analysis: Intermediate Terms......Page 1725
Interval Analysis: Nondifferentiable Problems......Page 1728
Interval Analysis for Optimization of Dynamical Systems......Page 1731
Interval Analysis: Parallel Methods for Global Optimization......Page 1738
Interval Analysis: Subdivision Directions in Interval Branch and Bound Methods......Page 1746
Interval Analysis: Systems of Nonlinear Equations......Page 1750
Interval Analysis: Unconstrained and Constrained Optimization......Page 1756
Interval Analysis: Verifying Feasibility......Page 1759
Interval Constraints......Page 1762
Interval Fixed Point Theory......Page 1765
Interval Global Optimization......Page 1768
Interval Linear Systems......Page 1786
Interval Newton Methods......Page 1792
Inventory Management in Supply Chains......Page 1795
Invexity and its Applications......Page 1799
Isotonic Regression Problems......Page 1803
Jaynes’ Maximum Entropy Principle......Page 1807
Job-shop Scheduling Problem......Page 1810
Kantorovich, Leonid Vitalyevich......Page 1817
Kolmogorov Complexity......Page 1818
Kuhn–Tucker Optimality Conditions......Page 1822
Lagrange, Joseph-Louis......Page 1826
Lagrange-Type Functions......Page 1827
Lagrangian Duality: BASICS......Page 1832
Lagrangian Multipliers Methods for Convex Programming......Page 1840
Laplace Method and Applications to Optimization Problems......Page 1845
Large Scale Trust Region Problems......Page 1849
Large Scale Unconstrained Optimization......Page 1858
L-convex Functions andM-convex Functions......Page 1865
LCP: Pardalos–Rosen Mixed Integer Formulation......Page 1872
Least-index Anticycling Rules......Page 1874
Least Squares Orthogonal Polynomials......Page 1878
Least Squares Problems......Page 1883
Leibniz, Gottfried Wilhelm......Page 1893
Lemke Method......Page 1895
Lexicographic Pivoting Rules......Page 1897
Linear Complementarity Problem......Page 1901
Linear Optimization: Theorems of the Alternative......Page 1905
Linear Ordering Problem......Page 1908
Linear Programming......Page 1910
Linear Programming: Interior Point Methods......Page 1913
Linear Programming: Karmarkar Projective Algorithm......Page 1916
Linear Programming: Klee–Minty Examples......Page 1918
Linear Programming Models for Classification......Page 1924
Linear Space......Page 1928
Lipschitzian Operators in Best Approximation by Bounded or Continuous Functions......Page 1929
Load Balancing for Parallel Optimization Techniques......Page 1932
Local Attractors for Gradient-related Descent Iterations......Page 1938
Location Routing Problem......Page 1946
Logconcave Measures, Logconvexity......Page 1952
Logconcavity of Discrete Distributions......Page 1954
Logic-Based Outer Approximation......Page 1955
Lovász Number......Page 1959
LP Strategy for Interval-Newton Method in Deterministic Global Optimization......Page 1964
L-shapedMethod for Two-stage Stochastic Programs with Recourse......Page 1970
Maritime Inventory Routing Problems......Page 1973
Mathematical Programming for DataMining......Page 1981
Mathematical Programming Methods in Supply Chain Management......Page 1985
Matrix Completion Problems......Page 1993
Matroids......Page 2001
Maximum Constraint Satisfaction: Relaxations and Upper Bounds......Page 2007
Maximum Cut Problem, MAX-CUT......Page 2017
Maximum Entropy and Game Theory......Page 2025
Maximum Entropy Principle: Image Reconstruction......Page 2030
Maximum Flow Problem......Page 2035
Maximum Likelihood Detection via Semidefinite Programming......Page 2046
Maximum Partition Matching......Page 2055
Maximum Satisfiability Problem......Page 2061
Medium-Term Scheduling of Batch Processes......Page 2067
Metaheuristic Algorithms for the Vehicle Routing Problem......Page 2081
Metaheuristics......Page 2087
Minimax: Directional Differentiability......Page 2101
Minimax Game Tree Searching......Page 2105
Minimax Theorems......Page 2113
Minimum Concave Transportation Problems......Page 2119
Minimum Cost Flow Problem......Page 2121
MINLP: Application in Facility Location-allocation......Page 2134
MINLP: Applications in Blending and Pooling Problems......Page 2140
MINLP: Applications in the Interaction of Design and Control......Page 2147
MINLP: Branch and Bound Global Optimization Algorithm......Page 2158
MINLP: Branch and Bound Methods......Page 2164
MINLP: Design and Scheduling of Batch Processes......Page 2168
MINLP: Generalized Cross Decomposition......Page 2174
MINLP: Global Optimization with αBB......Page 2181
MINLP: Heat Exchanger Network Synthesis......Page 2189
MINLP: Logic-based Methods......Page 2196
MINLP: Mass and Heat Exchanger Networks......Page 2199
MINLP: Outer Approximation Algorithm......Page 2205
MINLP: Reactive Distillation Column Synthesis......Page 2209
MINLP: Trim-loss Problem......Page 2216
Mixed 0-1 Linear Programming Approach for DNA Transcription Element Identification......Page 2225
Mixed Integer Classification Problems......Page 2236
Mixed Integer Linear Programming: Heat Exchanger Network Synthesis......Page 2240
Mixed Integer Linear Programming: Mass and Heat Exchanger Networks......Page 2243
Mixed Integer Nonlinear Bilevel Programming: Deterministic Global Optimization......Page 2251
Mixed-Integer Nonlinear Optimization: A Disjunctive Cutting Plane Approach......Page 2256
Mixed Integer Nonlinear Programming......Page 2260
Mixed Integer Optimization in Well Scheduling......Page 2273
Mixed Integer Programming/Constraint Programming Hybrid Methods......Page 2296
Model Based Control for Drug Delivery Systems......Page 2302
Modeling Difficult Optimization Problems......Page 2310
Modeling Languages in Optimization: A New Paradigm......Page 2323
Molecular Distance Geometry Problem......Page 2331
Molecular Structure Determination: Convex Global Underestimation......Page 2337
Monotonic Optimization......Page 2342
Monte-Carlo Simulated Annealing in Protein Folding......Page 2349
Monte-Carlo Simulations for Stochastic Optimization......Page 2363
Motzkin Transposition Theorem......Page 2371
Multi-Class Data Classification via Mixed-Integer Optimization......Page 2374
Multicommodity Flow Problems......Page 2380
Multicriteria Decision Support Methodologies for Auditing Decisions......Page 2388
Multicriteria Methods for Mergers and Acquisitions......Page 2398
Multicriteria Sorting Methods......Page 2405
Multidimensional Assignment Problem......Page 2422
Multidimensional Knapsack Problems......Page 2428
Multidisciplinary Design Optimization......Page 2432
Multifacility and Restricted Location Problems......Page 2435
Multi-index Transportation Problems......Page 2439
Multilevel Methods for Optimal Design......Page 2445
Multilevel Optimization in Mechanics......Page 2454
Multi-objective Combinatorial Optimization......Page 2463
Multi-objective Fractional Programming Problems......Page 2468
Multi-objective Integer Linear Programming......Page 2474
Multi-objective Mixed Integer Programming......Page 2480
Multi-objective Optimization and Decision Support Systems......Page 2486
Multi-objective Optimization: Interaction of Design and Control......Page 2491
Multi-objectiveOptimization: InteractiveMethods for Preference Value Functions......Page 2497
Multi-objective Optimization: Lagrange Duality......Page 2500
Multi-objective Optimization: Pareto Optimal Solutions, Properties......Page 2504
Multiparametric Linear Programming......Page 2508
Multiparametric Mixed Integer Linear Programming......Page 2510
Multiple Minima Problem in Protein Folding: αBB Global Optimization Approach......Page 2516
Multiple Objective Dynamic Programming......Page 2523
Multiple Objective Programming Support......Page 2529
Multiplicative Programming......Page 2537
Multi-Quadratic Integer Programming: Models and Applications......Page 2539
Multi-Scale Global Optimization Using Terrain/Funneling Methods......Page 2546
Multistage Stochastic Programming: Barycentric Approximation......Page 2553
Nested Partitions Optimization......Page 2558
Network Design Problems......Page 2564
Network Location: Covering Problems......Page 2570
Neural Networks for Combinatorial Optimization......Page 2572
Neuro-Dynamic Programming......Page 2580
New Hybrid Conjugate Gradient Algorithms for Unconstrained Optimization......Page 2585
Nonconvex Energy Functions: Hemivariational Inequalities......Page 2596
Nonconvex Network Flow Problems......Page 2603
Nonconvex-nonsmooth Calculus of Variations......Page 2606
Nondifferentiable Optimization......Page 2609
Nondifferentiable Optimization: Cutting PlaneMethods......Page 2615
Nondifferentiable Optimization: Minimax Problems......Page 2620
Nondifferentiable Optimization: Newton Method......Page 2627
Nondifferentiable Optimization: Parametric Programming......Page 2632
Nondifferentiable Optimization: Relaxation Methods......Page 2640
Nondifferentiable Optimization: Subgradient Optimization Methods......Page 2643
Nonlinear Least Squares: Newton-type Methods......Page 2644
Nonlinear Least Squares Problems......Page 2651
Nonlinear Least Squares: Trust Region Methods......Page 2655
Nonlinear Systems of Equations: Application to the Enclosure of All Azeotropes......Page 2662
Nonlocal Sensitivity Analysis with Automatic Differentiation......Page 2667
Nonoriented Multicommodity Flow Problems......Page 2672
Nonsmooth Analysis: Fréchet Subdifferentials......Page 2676
Nonsmooth Analysis: Weak Stationarity......Page 2683
Nonsmooth Optimization Approach to Clustering......Page 2690
Nonsmooth and Smoothing Methods for Nonlinear Complementarity Problems and Variational Inequalities......Page 2696
NP-complete Problems and Proof Methodology......Page 2700
Numerical Methods for Unary Optimization......Page 2707
Oligopolistic Market Equilibrium......Page 2715
Operations Research......Page 2718
Operations Research and Financial Markets......Page 2720
Operations Research Models for Supply Chain Management and Design......Page 2728
Optimal Control of a Flexible Arm......Page 2739
Optimal Design of Composite Structures......Page 2742
Optimal Design in Nonlinear Optics......Page 2749
Optimality Criteria for Multiphase Chemical Equilibrium......Page 2755
Optimal Planning of Offshore Oilfield Infrastructure......Page 2762
Optimal Sensor Scheduling......Page 2770
Optimal Solvent Design Approaches......Page 2774
Optimal Triangulations......Page 2781
Optimization in Ad Hoc Networks......Page 2788
Optimization Based Framework for Radiation Therapy......Page 2798
Optimization-Based Visualization......Page 2809
Optimization in Boolean Classification Problems......Page 2815
Optimization in Classifying Text Documents......Page 2820
Optimization and Decision Support Systems......Page 2827
Optimization with Equilibrium Constraints: A Piecewise SQP Approach......Page 2831
Optimization in Leveled Graphs......Page 2837
Optimization in Medical Imaging......Page 2844
Optimization in Operation of Electric and Energy Power Systems......Page 2848
Optimization Problems in Unit-Disk Graphs......Page 2856
Optimization Software......Page 2868
Optimization Strategies for Dynamic Systems......Page 2871
Optimization Techniques for Phase Retrieval Based on Single-Crystal X-Ray Diffraction Data......Page 2882
Optimization in Water Resources......Page 2887
Optimizing Facility Location with Euclidean and Rectilinear Distances......Page 2893
Order Complementarity......Page 2897
Oriented Matroids......Page 2902
Orthogonal Triangularization......Page 2910
Outranking Methods......Page 2911
Overdetermined Systems of Linear Equations......Page 2918
Packet Annealing......Page 2921
Parallel Computing: Complexity Classes......Page 2924
Parallel Computing: Models......Page 2927
Parallel Heuristic Search......Page 2932
Parametric Global Optimization: Sensitivity......Page 2936
Parametric Linear Programming: Cost Simplex Algorithm......Page 2941
Parametric Mixed Integer Nonlinear Optimization......Page 2944
Parametric Optimization: Embeddings, Path Following and Singularities......Page 2948
Peptide Identification via Mixed-Integer Optimization......Page 2954
Performance Profiles of Conjugate-Gradient Algorithms for Unconstrained Optimization......Page 2962
Phase Problem in X-ray Crystallography: Shake and Bake Approach......Page 2977
Piecewise Linear Network Flow Problems......Page 2982
Pivoting Algorithms for Linear Programming Generating Two Paths......Page 2989
Planning in the Process Industry......Page 2994
Plant Layout Problems and Optimization......Page 3003
Pontryagin Maximum Principle......Page 3011
Portfolio Selection: Markowitz Mean-variance Model......Page 3014
Portfolio Selection and Multicriteria Analysis......Page 3020
Potential Reduction Methods for Linear Programming......Page 3032
Powell Method......Page 3036
Practical Augmented Lagrangian Methods......Page 3038
Predictive Method for Interhelical Contacts in Alpha-Helical Proteins......Page 3047
Preference Disaggregation......Page 3055
Preference Disaggregation Approach: Basic Features, Examples fromFinancial DecisionMaking......Page 3066
Preference Modeling......Page 3079
Preprocessing in Stochastic Programming......Page 3082
Price of Robustness for Linear Optimization Problems......Page 3085
Principal Pivoting Methods for Linear Complementarity Problems......Page 3091
Probabilistic Analysis of Simplex Algorithms......Page 3097
Probabilistic Constrained Linear Programming: Duality Theory......Page 3108
Probabilistic Constrained Problems: Convexity Theory......Page 3111
Production-Distribution System Design Problem......Page 3112
Protein Folding: Generalized-Ensemble Algorithms......Page 3122
Protein Loop Structure Prediction Methods......Page 3124
Pseudomonotone Maps: Properties and Applications......Page 3129
QBB Global Optimization Method......Page 3135
QR Factorization......Page 3140
Quadratic Assignment Problem......Page 3143
Quadratic Fractional Programming: Dinkelbach Method......Page 3173
Quadratic Integer Programming: Complexity and Equivalent Forms......Page 3177
Quadratic Knapsack......Page 3183
Quadratic Programming with Bound Constraints......Page 3185
Quadratic Programming over an Ellipsoid......Page 3190
Quadratic Semi-assignment Problem......Page 3194
Quasidifferentiable Optimization......Page 3195
Quasidifferentiable Optimization: Algorithms for Hypodifferentiable Functions......Page 3200
Quasidifferentiable Optimization: Algorithms for QD Functions......Page 3202
Quasidifferentiable Optimization: Applications......Page 3208
Quasidifferentiable Optimization: Applications to Thermoelasticity......Page 3211
Quasidifferentiable Optimization: Calculus of Quasidifferentials......Page 3214
Quasidifferentiable Optimization: Codifferentiable Functions......Page 3218
Quasidifferentiable Optimization: Dini Derivatives, Clarke Derivatives......Page 3221
Quasidifferentiable Optimization: Exact Penalty Methods......Page 3224
Quasidifferentiable Optimization: Optimality Conditions......Page 3229
Quasidifferentiable Optimization: Stability of Dynamic Systems......Page 3237
Quasidifferentiable Optimization: Variational Formulations......Page 3241
Quasivariational Inequalities......Page 3245
Railroad Crew Scheduling......Page 3251
Railroad Locomotive Scheduling......Page 3260
Random Search Methods......Page 3269
Reactive Scheduling of Batch Processes......Page 3275
Redundancy in Nonlinear Programs......Page 3286
Reformulation-Linearization Technique for Global Optimization......Page 3287
Regression by Special Functions: Algorithms and Complexity......Page 3292
Relaxation in Projection Methods......Page 3297
Replicator Dynamics in Combinatorial Optimization......Page 3303
Resource Allocation for Epidemic Control......Page 3315
Reverse Convex Optimization......Page 3319
Robust Control......Page 3324
Robust Control: Schur Stability of Polytopes of Polynomials......Page 3329
Robust Design of Dynamic Systems by Constructive Nonlinear Dynamics......Page 3331
Robust Global Optimization......Page 3338
Robust Linear Programming with Right-Hand-Side Uncertainty, Duality and Applications......Page 3341
Robust Optimization......Page 3351
Robust Optimization: Mixed-Integer Linear Programs......Page 3355
Rosenbrock Method......Page 3367
Rosen’sMethod, Global Convergence, and Powell’s Conjecture......Page 3369
Saddle Point Theory and Optimality Conditions......Page 3379
Second Order Constraint Qualifications......Page 3381
Second Order Optimality Conditions for Nonlinear Optimization......Page 3385
Selection of Maximally Informative Genes......Page 3389
Selfdual Parametric Method for Linear Programs......Page 3398
Semidefinite Programming and Determinant Maximization......Page 3399
Semidefinite Programming: Optimality Conditions and Stability......Page 3404
Semidefinite Programming and the Sensor Network Localization Problem, SNLP......Page 3409
Semidefinite Programming and Structural Optimization......Page 3414
Semi-infinite Programming and Applications in Finance......Page 3420
Semi-infinite Programming: Approximation Methods......Page 3429
Semi-infinite Programming and Control Problems......Page 3432
Semi-infinite Programming: Discretization Methods......Page 3441
Semi-infinite Programming: Methods for Linear Problems......Page 3448
Semi-infinite Programming: Numerical Methods......Page 3453
Semi-infinite Programming: Second Order Optimality Conditions......Page 3458
Semi-infinite Programming, Semidefinite Programming and Perfect Duality......Page 3463
Sensitivity Analysis of Complementarity Problems......Page 3469
Sensitivity Analysis of Variational Inequality Problems......Page 3471
Sensitivity and Stability in NLP......Page 3474
Sensitivity and Stability in NLP: Approximation......Page 3478
Sensitivity and Stability in NLP: Continuity and Differential Stability......Page 3491
Sequential Cutting Plane Algorithm......Page 3495
Sequential Quadratic Programming: Interior PointMethods for DistributedOptimal Control Problems......Page 3500
Sequential Simplex Method......Page 3503
Set Covering, Packing and Partitioning Problems......Page 3506
Set-valued Optimization......Page 3510
Shape Optimization......Page 3512
Shape Reconstruction Methods for Nonconvex Feasibility Analysis......Page 3515
Shape Selective Zeolite Separation and Catalysis: Optimization Methods......Page 3524
Shor, Naum Zuselevich......Page 3529
Shortest Path Tree Algorithms......Page 3531
Short-Term Scheduling of Batch Processes with Resources......Page 3543
Short-Term Scheduling of Continuous Processes......Page 3557
Short-Term Scheduling, Resource Constrained: UnifiedModeling Frameworks......Page 3571
Short-Term Scheduling Under Uncertainty: Sensitivity Analysis......Page 3584
Signal Processing with Higher Order Statistics......Page 3591
Simple Recourse Problem: Dual Method......Page 3595
Simple Recourse Problem: Primal Method......Page 3597
Simplicial Decomposition......Page 3599
Simplicial Decomposition Algorithms......Page 3603
Simplicial Pivoting Algorithms for Integer Programming......Page 3609
Simulated Annealing......Page 3615
Simulated Annealing Methods in Protein Folding......Page 3617
Simultaneous Estimation and Optimization of Nonlinear Problems......Page 3622
Single Facility Location: Circle Covering Problem......Page 3631
Single Facility Location: Multi-objective Euclidean Distance Location......Page 3634
Single Facility Location: Multi-objective Rectilinear Distance Location......Page 3637
Smoothing Methods for Semi-Infinite Optimization......Page 3641
Smooth Nonlinear Nonconvex Optimization......Page 3646
Solution Methods for Multivalued Variational Inequalities......Page 3649
Solving Hemivariational Inequalities by Nonsmooth Optimization Methods......Page 3663
Solving Large Scale and Sparse Semidefinite Programs......Page 3667
Spatial Price Equilibrium......Page 3671
Spectral Projected Gradient Methods......Page 3676
Splitting Method for Linear Complementarity Problems......Page 3683
SSC Minimization Algorithms......Page 3686
SSC Minimization Algorithms for Nonsmooth and Stochastic Optimization......Page 3689
Stabilization of Cutting Plane Algorithms for Stochastic Linear Programming Problems......Page 3693
Stable Set Problem: Branch & Cut Algorithms......Page 3700
Standard Quadratic Optimization Problems: Algorithms......Page 3712
Standard Quadratic Optimization Problems: Applications......Page 3714
Standard Quadratic Optimization Problems: Theory......Page 3716
State of the Art inModeling Agricultural Systems......Page 3718
Static Resource Constrained Project Scheduling......Page 3728
Static Stochastic Programming Models......Page 3732
Static Stochastic Programming Models: Conditional Expectations......Page 3734
Statistical Classification: Optimization Approaches......Page 3735
Statistical Convergence and Turnpike Theory......Page 3737
Steiner Ratio of Biomolecular Structures......Page 3742
Steiner Tree Problems......Page 3747
Stochastic Bilevel Programs......Page 3760
Stochastic Global Optimization: Stopping Rules......Page 3767
Stochastic Global Optimization: Two-PhaseMethods......Page 3770
Stochastic Integer Programming: Continuity, Stability, Rates of Convergence......Page 3774
Stochastic Integer Programs......Page 3777
Stochastic Linear Programming: Decomposition and Cutting Planes......Page 3779
Stochastic Linear Programs with Recourse and Arbitrary Multivariate Distributions......Page 3784
Stochastic Network Problems: Massively Parallel Solution......Page 3789
Stochastic Optimal Stopping: Numerical Methods......Page 3797
Stochastic Optimal Stopping: Problem Formulations......Page 3799
Stochastic Programming: Minimax Approach......Page 3802
Stochastic Programming Models: Random Objective......Page 3806
Stochastic Programming: Nonanticipativity and Lagrange Multipliers......Page 3807
Stochastic Programming: Parallel Factorization of Structured Matrices......Page 3814
Stochastic Programming with Simple Integer Recourse......Page 3819
Stochastic Programs with Recourse: Upper Bounds......Page 3821
Stochastic Quasigradient Methods......Page 3826
Stochastic Quasigradient Methods: Applications......Page 3831
Stochastic Quasigradient Methods inMinimax Problems......Page 3837
Stochastic Scheduling......Page 3842
Stochastic Transportation and Location Problems......Page 3848
Stochastic Vehicle Routing Problems......Page 3853
Structural Optimization......Page 3856
Structural Optimization: History......Page 3858
Suboptimal Control......Page 3860
Successive Quadratic Programming......Page 3863
Successive Quadratic Programming: Applications in Distillation Systems......Page 3870
Successive Quadratic Programming: Applications in the Process Industry......Page 3877
Successive Quadratic Programming: Decomposition Methods......Page 3890
Successive Quadratic Programming: Full Space Methods......Page 3895
Successive Quadratic Programming: Solution by Active Sets and Interior Point Methods......Page 3902
Supply Chain Performance Measurement......Page 3908
Survivable Networks......Page 3913
Symmetric Systems of Linear Equations......Page 3916
Theorems of the Alternative and Optimization......Page 3919
Time-Dependent Traveling Salesman Problem......Page 3926
Topological Derivative in Shape Optimization......Page 3932
Topological Methods in Complementarity Theory......Page 3942
Topology of Global Optimization......Page 3946
Topology Optimization......Page 3952
Traffic Network Equilibrium......Page 3953
Traveling Salesman Problem......Page 3959
Tucker Homogeneous Systems of Linear Relations......Page 3968
Turnpike Theory: Stability of Optimal Trajectories......Page 3972
Two-Stage Stochastic Programming: Quasigradient Method......Page 3979
Two-Stage Stochastic Programs with Recourse......Page 3983
Unconstrained Nonlinear Optimization: Newton–Cauchy Framework......Page 3986
Unconstrained Optimization in Neural Network Training......Page 3991
Variable Neighborhood Search Methods......Page 3998
Variational Inequalities......Page 4012
Variational Inequalities: F. E. Approach......Page 4017
Variational Inequalities: Geometric Interpretation, Existence and Uniqueness......Page 4022
Variational Inequalities: Projected Dynamical System......Page 4025
Variational Principles......Page 4030
Vector Optimization......Page 4034
Vector Variational Inequalities......Page 4037
Vehicle Routing......Page 4042
Vehicle Routing Problem with Simultaneous Pickups and Deliveries......Page 4045
Vehicle Scheduling......Page 4050
Volume Computation for Polytopes: Strategies and Performances......Page 4055
Von Neumann, John......Page 4061
Voronoi Diagrams in Facility Location......Page 4063
Walrasian Price Equilibrium......Page 4069
Warehouse Location Problem......Page 4072
Wastewater System, Optimization of......Page 4077
Young Programming......Page 4083
Preface to the Index Volume......Page 4090
Subject Index......Page 4092
A......Page 4093
B......Page 4118
C......Page 4137
D......Page 4178
E......Page 4209
F......Page 4227
G......Page 4247
H......Page 4270
I......Page 4282
J......Page 4309
K......Page 4310
L......Page 4315
M......Page 4341
N......Page 4390
O......Page 4413
P......Page 4429
Q......Page 4475
R......Page 4487
S......Page 4508
T......Page 4577
U......Page 4595
V......Page 4602
W......Page 4612
Z......Page 4617
A......Page 4619
B......Page 4620
C......Page 4621
D......Page 4623
E......Page 4624
F......Page 4625
G......Page 4626
H......Page 4627
J......Page 4629
K......Page 4630
L......Page 4632
M......Page 4633
N......Page 4635
P......Page 4636
R......Page 4638
S......Page 4639
T......Page 4642
V......Page 4643
W......Page 4644
Y......Page 4645
Z......Page 4646