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