Taiwanese Journal of Mathematics

GAP FUNCTIONS FOR NONSMOOTH EQUILIBRIUM PROBLEMS

Marco Castellani and Massimo Pappalardo

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Abstract

We consider equilibrium problems (EP) with directionally differentiable (not necessarily ${\mathcal C}^1$) bifunctions which are convex with respect to the second variable and we use a gap function approach to solve them. In the first part of the paper we establish a condition under which any stationary point of the gap function solves (EP) and we propose a solution method which uses descent directions of the gap function. In the final section we study the problem when this condition is not satisfied. In this case we use a family of gap functions depending on a parameter $\alpha$ which allows us to overcome the trouble due to the lack of a descent direction.

Article information

Source
Taiwanese J. Math., Volume 13, Number 6A (2009), 1837-1846.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405616

Digital Object Identifier
doi:10.11650/twjm/1500405616

Mathematical Reviews number (MathSciNet)
MR2583743

Zentralblatt MATH identifier
1219.90170

Subjects
Primary: 90C30: Nonlinear programming 49M37: Methods of nonlinear programming type [See also 90C30, 65Kxx]

Keywords
equilibrium problems gap functions

Citation

Castellani, Marco; Pappalardo, Massimo. GAP FUNCTIONS FOR NONSMOOTH EQUILIBRIUM PROBLEMS. Taiwanese J. Math. 13 (2009), no. 6A, 1837--1846. doi:10.11650/twjm/1500405616. https://projecteuclid.org/euclid.twjm/1500405616


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