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2009•Journal of Weifang UniversityRequires access

A Derivative-free Descent Method for Solving Quasi-variational Inequality Problem

Biao Qu

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Abstract

Constructing a descent direction obtained from the directional differentiability of the(generalized) regularized gap function,we present a derivative-free descent method for solving the quasi-variational inequality problem in this paper.We do not need consider the gradient problem of the objection function.Compared with the ones in the related references,the method of this paper has the superiority that the application is more wider.Under some reasonable conditions,the convergence of the algorithm is proved.

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What this paper is about

Constructing a descent direction obtained from the directional differentiability of the(generalized) regularized gap function,we present a derivative-free descent method for solving the quasi-variational inequality problem in this paper.We do not need consider the gradient problem of the objection function.Compared with the ones in the related references,the method of this paper has the superiority that the application is more wider.Under some reasonable conditions,the convergence of the algorithm is proved.

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Available abstract

Constructing a descent direction obtained from the directional differentiability of the(generalized) regularized gap function,we present a derivative-free descent method for solving the quasi-variational inequality problem in this paper.We do not need consider the gradient problem of the objection function.Compared with the ones in the related references,the method of this paper has the superiority that the application is more wider.Under some reasonable conditions,the convergence of the algorithm is proved.

Key concepts: Descent (aeronautics), Variational inequality, Descent direction, Directional derivative, Differentiable function, Mathematics, Convergence (economics), Gradient descent

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