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Finite convergence and weak sharpness for solutions of nonsmooth variational inequalities in Hilbert spaces

Luong Nguyen (luonghdu***at***gmail.com)
Qamrul Hasan Ansari (qhansari***at***gmail.com)
Xiaolong Qin (qxlxajh***at***163.com)

Abstract: This paper deals with the study of weak sharp solutions for nonsmooth variational inequalities and finite convergence property of the proximal point method. We present several characterizations for weak sharpness of the solutions set of nonsmooth variational inequalities without using the gap functions. We show that under weak sharpness of the solutions set, the sequence generated by proximal point methods terminates after a finite number of iterations. We also give an upper bound for the number of iterations for which the sequence generated by the exact proximal point methods terminates.

Keywords: Convex programming, Nonsmooth variational inequalities, Weak sharp solutions, Finite convergence property, Pseudomonotone operators, Proximal point method.

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization


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Entry Submitted: 07/07/2018
Entry Accepted: 07/07/2018
Entry Last Modified: 07/07/2018

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