Author(s): Leon Cooper, David Steinberg
Publisher: W B Saunders Co
Year: 1970
Language: English
Pages: viii & 381
Cover
Copyright
Preface
Contents
INTRODUCTION
1.1 Introduction
1.2 Set Notation
MATRIX ALGEBRA
2.1 Introduction
2.2 Matrices
2.3 Operations with Matrices: Addition, Scalar Multiplication, and Subtraction
2.4 Multiplication of Matrices
2.5 Special Types of Matrices
2.6 Partitioned Matrices
2.7 Determinants
2.8 Rank
2.9 Systems of m Equations in n Unknowns
2.10 Systems of n Equations in n Unknowns
2.11 Linear Independence ; Vector Spaces
2.12 Quadratic Forms and Definite Matrices
n-DIMENSIONAL GEOMETRY AND CONVEX SETS
3.1 Introduction: Hyperplanes
3.2 Hyperspheres; Open, Closed and Bounded Sets
3.3 Convex Sets
3.4 Convex Hulls and Convex Polyhedra
3.5 Separating and Supporting Hyperplanes
CLASSICAL OPTIMIZATION
4.1 Introduction
4.2 Functions of One Variable: Mathematical Background
4.3 Optimization of Functions of a Single Variable
4.4 Sufficient Conditions for the Existence of an Optimum
4.5 Global Extrema: One Variable
4.6 Numerical Problems of Root Finding
4.7 Optima of Convex and Concave Functions
4.8 Optimization of Functions of Several Variables: Mathematical Background
4.9 Optimization of Functions of More Than One Variable
4.10 Global Extrema: Many Variables
4.11 Optima of Convex and Concave Functions
4.12 Constrained Optimization
4.13 Examples of Constrained Optimization
4.14 Inequality Constraints
SEARCH TECHNIQUES: UNCONSTRAINED PROBLEMS
5.1 Introduction
5.2 The One-Dimensional Search Problem
5.3 Simultaneous Methods: One-Dimensional Search
5.4 One-Dimensional Sequential Methods
5.5 Dichotomous Search
5.6 Equal Interval Search
5.7 Fibonacci Search
5.8 The Multidimensional Search Problem
5.9 Simultaneous Methods -- Multidimensional Search
5.10 Multidimensional Sequential Methods
5.11 Multivariate Grid Search
5.12 Univariate Search Method
5.13 Powell's Method
5.14 Method of Steepest Descent
5.15 The Fletcher-Powell Method
5.16 Pattern Search
LINEAR PROGRAMMING
6.1 Introduction
6.2 Geometric Interpretation of Linear Programming
6.3 How Not To Solve a Linear Programming Problem
6.4 The Simplex Method: Basic Theorems
6.5 The Simplex Method: Theory
6.6 The Simplex Method: Computational Techniques
LINEAR PROGRAMMING: ADDITIONAL TOPICS
7.1 The Theory of Duality in Linear Programming
7.2 Other Simplex Algorithms
7.3 The Decomposition Principle
7.4 Postoptimal Analysis
7.5 The Transportation Problem
7.6 Network Flow Problems
NONLINEAR PROGRAMMING
8.1 Introduction
8.2 Convex Constraint Sets
8.3 The Kuhn-Tucker Conditions
8.4 Quadratic Programming
8.5 Separable Programming
8.6 Gradient Methods
8.7 The Method of Griffith and Stewart
INTEGER PROGRAMMING
9.1 Introduction
9.2 Formulation of Models as Integer Programming Problems
9.3 Gomory's Algorithm
9.4 The Bounded Variable Algorithm
9.5 Branch and Bound Methods
9.6 Dynamic Programming: Introduction
9.7 Dynamic Programming: General Discussion; An Example
ANSWERS TO SELECTED EXERCISES
INDEX
