Optimization Toolbox Using the Optimization Toolbox Preface What Is the Optimization Toolbox? New Features in Version 2.1 Toolbox Speed Function Handles Large Structured Problems Using This Guide Acknowledgments Related Products Configuration Information Technical Conventions Matrix, Vector, and Scalar Notation Typographical Conventions Tutorial Overview Introduction Problems Covered by the Toolbox Using the Optimization Functions Examples that Use Standard Algorithms Unconstrained Example Nonlinear Inequality Constrained Example Constrained Example with Bounds Constrained Example with Gradients Gradient Check: Analytic Versus Numeric Equality Constrained Example Maximization Greater-Than-Zero Constraints Additional Arguments: Avoiding Global Variables Multiobjective Examples Large-Scale Examples Problems Covered by Large-Scale Methods Nonlinear Equations with Jacobian Nonlinear Equations with Jacobian Sparsity Pattern Nonlinear Least Squares with Full Jacobian Sparsity Pattern Nonlinear Minimization with Gradient and Hessian Nonlinear Minimization with Gradient and Hessian Sparsity Pattern Nonlinear Minimization with Bound Constraints and Banded Preconditioner Nonlinear Minimization with Equality Constraints Nonlinear Minimization with a Dense but Structured Hessian and Equality Constraints Quadratic Minimization with Bound Constraints Quadratic Minimization with a Dense but Structured Hessian Linear Least Squares with Bound Constraints Linear Programming with Equalities and Inequalities Linear Programming with Dense Columns in the Equalities Default Parameter Settings Changing the Default Settings Displaying Iterative Output Output Headings: Medium-Scale Algorithms Output Headings: Large-Scale Algorithms Optimization of Inline Objects Instead of M-Files Typical Problems and How to Deal with Them Converting Your Code to Version 2 Syntax Using optimset and optimget New Calling Sequences Example of Converting from constr to fmincon Selected Bibliography Standard Algorithms Overview Optimization Overview Unconstrained Optimization Quasi-Newton Methods Line Search Quasi-Newton Implementation Hessian Update Line Search Procedures Least Squares Optimization Gauss-Newton Method Levenberg-Marquardt Method Nonlinear Least Squares Implementation Gauss-Newton Implementation Levenberg-Marquardt Implementation Constrained Optimization Sequential Quadratic Programming (SQP) Quadratic Programming (QP) Subproblem SQP Implementation Updating the Hessian Matrix Quadratic Programming Solution Line Search and Merit Function Multiobjective Optimization Introduction Goal Attainment Method Algorithm Improvements for Goal Attainment Method Selected Bibliography Large-Scale Algorithms Overview Trust Region Methods for Nonlinear Minimization Preconditioned Conjugate Gradients Linearly Constrained Problems Linear Equality Constraints Box Constraints Nonlinear Least Squares Quadratic Programming Linear Least Squares Large-Scale Linear Programming Main Algorithm Preprocessing Selected Bibliography Index of Examples Reference Function Reference Functions by Category Minimization Equation Solving Least Squares (Curve Fitting) Utility Demos of Large-Scale Methods Demos of Medium-Scale Methods Function Arguments Optimization Options Parameters Alphabetical List of Functions fgoalattain fminbnd fmincon fminimax fminsearch fminunc fseminf fsolve fzero linprog lsqcurvefit lsqlin lsqnonlin lsqnonneg optimget optimset quadprog Printable Documentation (PDF) Product Page (Web)