Auxiliary Problem Principle On Variational Inequalities

• Main Authors: Pei-Min Tsai, 蔡佩旻
• Other Authors: Liang-Ju Chu
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/76705885271849518327

碩士 === 國立臺灣師範大學 === 數學研究所 === 90 === The auxiliary problem principle allows us to find the solution of an optimization problem (minimization problem, saddle-point problem, variational inequality problem, etc.) by solving a sequence of auxiliary problem. Following the auxiliary problem principle of Cohen, we introduce and analyze an algorithm to solve the usual variational inequality VI(T,C). In this paper, the concept of proximal method is introduced and a convergent algorithm is proposed for solving set-valued variational inequalities involving nonmonotone operators in reflexive Banach spaces. The aim of our work is to establish similar links for the auxiliary problem principle. In fact, the purpose of this paper has two folds : (1) We first deal with the convergence of algorithm based on the auxiliary problem principle under generalized monotonicity, such as, pseudo-Dunn property, strong pseudomonotonicity, $\alpha$-strong pseudomonotonicity, etc. (2) We present a modified algorithm for solving our variational inequalities under a weaker condition on the auxiliary function without strong monotonicity.