Plenary Lecture

Several Equivalent Relations about Variational Inequality Problems

Professor Zili Wu
Department of Mathematical Sciences
Xi'an Jiaotong-Liverpool University

Abstract: We consider equivalent relations between the Gateaux differentiabilities of two gap functions of variational inequality problems. Some equivalent conditions for their locally Lipschitz property are also presented. Equivalent condition for the relevant mapping to be pseudomonotone+ on relevant solutions sets are obtained. Based on the above results, we characterize the weak sharpness of the solutions of variational inequality problems in terms of error bounds of two gap functions. Furthermore we show that some algorithms for solving variational inequality problems possess finite convergence property.

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