What Is Optimization Toolbox?

Introductionresulting point where the maximum of f occurs is also the point where theminimum of -f occurs.Changing OptionsYou can change the default options for an optimization function by passingin an options structure, which you create using the function optimset, asan input argument. See “Default Options Settings” on page 2-78 for moreinformation.Supplying the GradientMany of the optimization functions use the gradient of the objective functionto search for the minimum. You can write a function that computes thegradient and pass it to an optimization function using the options structure.“Constrained Example with Gradients” onpage2-15providesanexampleofhow to do this. Providing a gradient function improves the accuracy and speedof the optimization function. However, for some objective functions it mightnot be possible to provide a gradient function, in which case the optimizationfunction calculates it using an adaptive finite-difference method.Medium- and Large-Scale AlgorithmsThis guide separates “medium-scale” algorithms from “large-scale”algorithms. Medium-scale is not a standard term and is used here only todistinguish these algorithms from the large-scale algorithms, which aredesigned to handle large-scale problems efficiently.Medium-Scale AlgorithmsOptimization Toolbox routines offer a choice of algorithms and line searchstrategies. The principal algorithms for unconstrained minimization arethe Nelder-Mead simplex search method and the BFGS (Broyden, Fletcher,Goldfarb, and Shanno) quasi-Newton method. For constrained minimization,minimax, goal attainment, and semi-infinite optimization, variations ofsequential quadratic programming (SQP) are used. Nonlinear least-squaresproblems use the Gauss-Newton and Levenberg-Marquardt methods.Nonlinear equation solving also uses the trust-region dogleg algorithm.2-7