Auxiliary Principle and Iterative Algorithms for Lions-Stampacchia Variational Inequalities

F. Q. Xia () and N. J. Huang ()
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F. Q. Xia: Sichuan Normal University
N. J. Huang: Sichuan University

Journal of Optimization Theory and Applications, 2009, vol. 140, issue 2, No 12, 377-389

Abstract: Abstract In this paper, we extend the auxiliary principle (Cohen in J. Optim. Theory Appl. 49:325–333, 1988) to study a class of Lions-Stampacchia variational inequalities in Hilbert spaces. Our method consists in approximating, in the subproblems, the nonsmooth convex function by a sequence of piecewise linear and convex functions, as in the bundle method for nonsmooth optimization. This makes the subproblems more tractable. We show the existence of a solution for this Lions-Stampacchia variational inequality and explain how to build a new iterative scheme and a new stopping criterion. This iterative scheme and criterion are different from those commonly used in the special case of nonsmooth optimization. We study also the convergence of iterative sequences generated by the algorithm.

Keywords: Lions-Stampacchia variational inequalities; Iterative schemes; Auxiliary principle technique; Stopping criterion; Strongly convex functions (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-008-9441-z

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