MDSMAX Multidirectional search method for direct search optimization. [x, fmax, nf] = MDSMAX(FUN, x0, STOPIT, SAVIT) attempts to maximize the function FUN, using the starting vector x0. The method of multidirectional search is used. Output arguments: x = vector yielding largest function value found, fmax = function value at x, nf = number of function evaluations. The iteration is terminated when either - the relative size of the simplex is <= STOPIT(1) (default 1e-3), - STOPIT(2) function evaluations have been performed (default inf, i.e., no limit), or - a function value equals or exceeds STOPIT(3) (default inf, i.e., no test on function values). The form of the initial simplex is determined by STOPIT(4): STOPIT(4) = 0: regular simplex (sides of equal length, the default), STOPIT(4) = 1: right-angled simplex. Progress of the iteration is not shown if STOPIT(5) = 0 (default 1). If a non-empty fourth parameter string SAVIT is present, then `SAVE SAVIT x fmax nf' is executed after each inner iteration. NB: x0 can be a matrix. In the output argument, in SAVIT saves, and in function calls, x has the same shape as x0. MDSMAX(fun, x0, STOPIT, SAVIT, P1, P2,...) allows additional arguments to be passed to fun, via feval(fun,x,P1,P2,...). This implementation uses 2n^2 elements of storage (two simplices), where x0 is an n-vector. It is based on the algorithm statement in [2, sec.3], modified so as to halve the storage (with a slight loss in readability). References: [1] V. J. Torczon, Multi-directional search: A direct search algorithm for parallel machines, Ph.D. Thesis, Rice University, Houston, Texas, 1989. [2] V. J. Torczon, On the convergence of the multidirectional search algorithm, SIAM J. Optimization, 1 (1991), pp. 123-145. [3] N. J. Higham, Optimization by direct search in matrix computations, SIAM J. Matrix Anal. Appl, 14(2): 317-333, 1993. [4] N. J. Higham, Accuracy and Stability of Numerical Algorithms, Second edition, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2002; sec. 20.5.
Package: optim