Convergence of the Approximate Auxiliary Problem Method for Solving Generalized Variational Inequalities

T. T. Hue, J. J. Strodiot and V. H. Nguyen
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T. T. Hue: University of Hue
J. J. Strodiot: Facultés Universitaires Notre Dame de la Paix
V. H. Nguyen: Facultés Universitaires Notre Dame de la Paix

Journal of Optimization Theory and Applications, 2004, vol. 121, issue 1, No 7, 119-145

Abstract: Abstract We consider an extension of the auxiliary problem principle for solving a general variational inequality problem. This problem consists in finding a zero of the sum of two operators defined on a real Hilbert space H: the first is a monotone single-valued operator; the second is the subdifferential of a lower semicontinuous proper convex function ϕ. To make the subproblems easier to solve, we consider two kinds of lower approximations for the function ϕ: a smooth approximation and a piecewise linear convex approximation. We explain how to construct these approximations and we prove the weak convergence and the strong convergence of the sequence generated by the corresponding algorithms under a pseudo Dunn condition on the single-valued operator. Finally, we report some numerical experiences to illustrate the behavior of the two algorithms.

Keywords: Variational inequalities; auxiliary problem principle; bundle methods; barrier methods; pseudo Dunn condition (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/B:JOTA.0000026134.57920.e1

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