Pattern Search Methods For Nonlinear Optimization Problems

Pattern Search Algorithm is the main work in the paper,which is a particular sub-set of direct search methods that neither compute nor approximate any derivatives,and consequently do not need to enforce explicitly a notion of sufficient decrease to guarantee the convergence.Thus,this class of methods is suitable for problems when the objectives are complicated or their derivatives are difficult to compute,it is widely applicable for nonlinear optimization problems.The main work in this paper is that we propose the generalized pattern search al-gorithm for two problems,first is the non-linear least-square problems;second is minimax Problems with non-linear inequality constraints.The main results,obtained in this disser-tation,may be summarized as follows1. Chapter 2 constructs pattern search algorithm for non-linear least-square prob-lems,use this method can get the global convergence results despite the explicit informa-tion concerning the first or second-order gradient.2. Chapter 3 constructs pattern search algorithm for minimax problem with non-linear inequality constraints.To solve the non-smoothness of the objective function,we convert it into an approximate smooth one by using a smoothing parameter,and propose the pattern search method and iterate in the feasible set for the approximate smooth problem,therefore get the stationary point of the original problem under some additional conditions.This method get the global convergence results also despite the explicit infor-mation concerning the first or second-order gradient.