Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Problems Covered by the Toolbox . . . . . . . . . . . . . . . . . . . . . . . . 2-3
Using the Optimization Functions . . . . . . . . . . . . . . . . . . . . . . . 2-5
ii Contents
Examples that Use Standard Algorithms . . . . . . . . . . . . . . . . 2-7
Unconstrained Minimization Example . . . . . . . . . . . . . . . . . . . . 2-8
Nonlinear Inequality Constrained Example . . . . . . . . . . . . . . . 2-9
Constrained Example with Bounds . . . . . . . . . . . . . . . . . . . . . 2-11
Constrained Example with Gradients . . . . . . . . . . . . . . . . . . . 2-12
Gradient Check: Analytic Versus Numeric . . . . . . . . . . . . . . . 2-14
Equality Constrained Example . . . . . . . . . . . . . . . . . . . . . . . . . 2-15
Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16
Greater-Than-Zero Constraints . . . . . . . . . . . . . . . . . . . . . . . . 2-16
Additional Arguments: Avoiding Global Variables . . . . . . . . . 2-16
Nonlinear Equations with Analytic Jacobian . . . . . . . . . . . . . . 2-17
Nonlinear Equations with Finite-Difference Jacobian . . . . . . 2-20
Multiobjective Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21
Large-Scale Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33
Problems Covered by Large-Scale Methods . . . . . . . . . . . . . . . 2-34
Nonlinear Equations with Jacobian . . . . . . . . . . . . . . . . . . . . . 2-37
Nonlinear Equations with Jacobian Sparsity Pattern . . . . . . . 2-39
Nonlinear Least-Squares with Full Jacobian Sparsity
Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-41
Nonlinear Minimization with Gradient and Hessian . . . . . . . 2-43
Nonlinear Minimization with Gradient and Hessian Sparsity
Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
Nonlinear Minimization with Bound Constraints and Banded
Preconditioner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-46
Nonlinear Minimization with Equality Constraints . . . . . . . . 2-50
Nonlinear Minimization with a Dense but Structured Hessian
and Equality Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-51
Quadratic Minimization with Bound Constraints . . . . . . . . . . 2-55
Quadratic Minimization with a Dense but Structured
Hessian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-57
Linear Least-Squares with Bound Constraints . . . . . . . . . . . . 2-60
Linear Programming with Equalities and Inequalities . . . . . . 2-61
Linear Programming with Dense Columns in the Equalities . 2-62
Default Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-65
Changing the Default Settings . . . . . . . . . . . . . . . . . . . . . . . . . 2-65
Displaying Iterative Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-68
Output Headings: Medium-Scale Algorithms . . . . . . . . . . . . . 2-68
iii
Output Headings: Large-Scale Algorithms . . . . . . . . . . . . . . . 2-71
Optimization of Inline Objects Instead of M-Files . . . . . . . 2-74
Typical Problems and How to Deal with Them . . . . . . . . . . 2-76
Converting Your Code to Version 2 Syntax . . . . . . . . . . . . . 2-80
Using optimset and optimget . . . . . . . . . . . . . . . . . . . . . . . . . . 2-81
New Calling Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-81
Example of Converting from constr to fmincon . . . . . . . . . . . . 2-89
Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-92
3
Standard Algorithms……
