Matlab - Optimisation Toolbox User's Guide

Preface......Page 9
Using This Guide......Page 10
Related Products......Page 11
Typographical Conventions......Page 13
Introduction......Page 15
What Is the Optimization Toolbox?......Page 16
New fsolve Default Algorithm......Page 17
Configuration Information......Page 18
Matrix, Vector, and Scalar Notation......Page 19
Acknowledgments......Page 20
Tutorial......Page 21
Problems Covered by the Toolbox......Page 23
Using the Optimization Functions......Page 25
Examples that Use Standard Algorithms......Page 27
Unconstrained Minimization Example......Page 28
Nonlinear Inequality Constrained Example......Page 29
Constrained Example with Bounds......Page 31
Constrained Example with Gradients......Page 32
Gradient Check: Analytic Versus Numeric......Page 34
Equality Constrained Example......Page 35
Additional Arguments: Avoiding Global Variables......Page 36
Nonlinear Equations with Analytic Jacobian......Page 37
Nonlinear Equations with Finite-Difference Jacobian......Page 40
Multiobjective Examples......Page 41
Large-Scale Examples......Page 53
Problems Covered by Large-Scale Methods......Page 54
Nonlinear Equations with Jacobian......Page 57
Nonlinear Equations with Jacobian Sparsity Pattern......Page 59
Nonlinear Least-Squares with Full Jacobian Sparsity Pattern......Page 61
Nonlinear Minimization with Gradient and Hessian......Page 63
Nonlinear Minimization with Gradient and Hessian Sparsity Pattern......Page 64
Nonlinear Minimization with Bound Constraints and Banded Preconditioner......Page 66
Nonlinear Minimization with Equality Constraints......Page 70
Nonlinear Minimization with a Dense but Structured Hessian and Equality Constraints......Page 71
Quadratic Minimization with Bound Constraints......Page 75
Quadratic Minimization with a Dense but Structured Hessian......Page 77
Linear Least-Squares with Bound Constraints......Page 80
Linear Programming with Equalities and Inequalities......Page 81
Linear Programming with Dense Columns in the Equalities......Page 82
Changing the Default Settings......Page 85
Output Headings: Medium-Scale Algorithms......Page 88
Output Headings: Large-Scale Algorithms......Page 91
Optimization of Inline Objects Instead of M-Files......Page 94
Typical Problems and How to Deal with Them......Page 96
Converting Your Code to Version 2 Syntax......Page 100
New Calling Sequences......Page 101
Example of Converting from constr to fmincon......Page 109
Selected Bibliography......Page 112
Standard Algorithms......Page 113
Optimization Overview......Page 115
Unconstrained Optimization......Page 116
Quasi-Newton Methods......Page 118
Line Search......Page 120
Quasi-Newton Implementation......Page 123
Least-Squares Optimization......Page 130
Gauss-Newton Method......Page 131
Levenberg-Marquardt Method......Page 132
Nonlinear Least-Squares Implementation......Page 134
Trust-Region Dogleg Method......Page 136
Nonlinear Equations Implementation......Page 138
Constrained Optimization......Page 140
Sequential Quadratic Programming (SQP)......Page 141
Quadratic Programming (QP) Subproblem......Page 142
SQP Implementation......Page 143
Introduction......Page 150
Goal Attainment Method......Page 156
Algorithm Improvements for Goal Attainment Method......Page 157
Selected Bibliography......Page 160
Large-Scale Algorithms......Page 165
Trust-Region Methods for Nonlinear Minimization......Page 166
Preconditioned Conjugate Gradients......Page 169
Box Constraints......Page 171
Nonlinear Least-Squares......Page 174
Quadratic Programming......Page 175
Linear Least-Squares......Page 176
Main Algorithm......Page 177
Preprocessing......Page 180
Selected Bibliography......Page 181
Function Reference......Page 183
Equation Solving......Page 184
Demos of Large-Scale Methods......Page 185
Demos of Medium-Scale Methods......Page 186
Function Arguments......Page 187
Optimization Options Parameters......Page 192
Functions — Alphabetical List......Page 197
fgoalattain......Page 198
fminbnd......Page 210
fmincon......Page 214
fminimax......Page 228
fminsearch......Page 237
fminunc......Page 241
fseminf......Page 251
fsolve......Page 264
fzero......Page 276
fzmult......Page 280
gangstr......Page 281
linprog......Page 282
lsqcurvefit......Page 290
lsqlin......Page 302
lsqnonlin......Page 310
lsqnonneg......Page 322
optimget......Page 326
optimset......Page 327
quadprog......Page 331
Index......Page 341