What Is Optimization Toolbox?

fminimaxset to 'iter'). The dependent equalities are only removed when theequalities are consistent. If the system of equalities is not consistent,the subproblem is infeasible and 'infeasible' is displayed under theProcedures heading.AlgorithmLimitationsReferencesfminimax internally reformulates the minimax problem into anequivalent Nonlinear Linear Programming problem by appendingadditional (reformulation) constraints of the form F i(x) ≤ γ to theconstraints given in “Equation” on page 8-54, and then minimizingγ over x. fminimax uses a sequential quadratic programming (SQP)method [1] to solve this problem.Modifications are made to the line search and Hessian. In the linesearch an exact merit function (see [2] and [4]) is used together with themerit function proposed by [3] and [5]. The line search is terminatedwhen either merit function shows improvement. The function usesa modified Hessian that takes advantage of the special structureof this problem. Using optimset to set the MeritFunction optionto'singleobj' uses the merit function and Hessian used in fmincon.Seealso“SQPImplementation”onpage3-32formoredetailsonthe algorithm used and the types of procedures printed under theProcedures heading when you set the Display option to'iter'.The function to be minimized must be continuous. fminimax mightonly give local solutions.[1] Brayton, R.K., S.W. Director, G.D. Hachtel, and L.Vidigal, “A NewAlgorithm for Statistical Circuit Design Based on Quasi-NewtonMethods and Function Splitting,” IEEE Trans. Circuits and Systems,Vol. CAS-26, pp. 784-794, Sept. 1979.[2] Grace, A.C.W., “Computer-Aided Control System Design UsingOptimization Techniques,” Ph.D. Thesis, University of Wales, Bangor,Gwynedd, UK, 1989.8-66