Research On Direct Search Algorithm For Derivative-free Optimization

It is well known that derivative is the very important information for optimization.Most optimization methods rely on the derivative information of the problem,but the derivative of the solving problems do not exist in many practical problems,or the derivative of the solving problems is difficult to obtain,so that some high-precision derivative optimization methods can not be used.We need to study the method of not using the derivative information,as an important optimization algorithm in the derivative-free optimization algorithm,the direct search method has got the favorite of the practical workers of science and engineering.This paper mainly research on the Coope-Price algorithm framework among direct search methods,based on the introduction and analysis of Coope-Price algorithm in the literature,which the corresponding improvement of some shortcomings and deficiencies exist in the framework.In view of the above analysis,this paper proposes two new direct search algorithms,combined with the relevant theory to analyze the convergence of the new algorithms,combined with numerical experiments to verify the effectiveness and feasibility of the algorithms.Four main direct search frameworks(Coope-Price,GPS,GSS and MADS)are analyzed and compared in the direct search algorithm.Furthermore,Aiming at the comparison of numerical experiments in the derivative-free algorithm,two important methods of derivative-free numerical algorithm are introduced.The two methods are described in detail,and the method is used to make a simple explanation.Finally,two new direct search algorithms are proposed based on Coope-Price algorithm framework.First,a new conjugate gradient descent direction is given based on the central simple gradient.At the same time,the positive basis of the grid cell frame is recalculated,and a direct search method based on the center simplex gradient is presented.Secondly,according to the adaptive BB(Barzilai-Borwein)step-size in the derivative-free,the update strategy of the grid step size in the Coope-Price algorithm framework is proposed,and a new grid step parameter updating strategy is proposed.Which effectively improves the problem that the grid step fall too fast in some cases.At the same time,combined with the advantage of the adaptive BB(Barzilai-Borwein)step-size,the corresponding positive basis updating strategy is given,a direct search conjugate gradient method for BB step size is proposed.Furthermore,the convergence of the two algorithms is proved theoretically,and the algorithm is validated by the numerical experiment.The new algorithms are compared and analyzed from the experimental results,and the validity of the two proposed algorithms is proved feasibility.