## Taiwanese Journal of Mathematics

### SUBOPTIMALITY CONDITIONS FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS

#### Abstract

In this paper we study mathematical programs with equilibrium constraints (MPECs) described by generalized equations in the extended form \begin{eqnarray*} 0\in G(x,y)+Q(x,y), \end{eqnarray*} where both mappings $G$ and $Q$ are set-valued. Such models arise, in particular, from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish new weak and strong suboptimality conditions for the general MPEC problems under consideration in finite-dimensional and infinite-dimensional spaces that do not assume the existence of optimal solutions. This issue is particularly important for infinite-dimensional optimization problems, where the existence of optimal solutions requires quite restrictive assumptions. Our techniques are mainly based on modern tools of variational analysis and generalized differentiation revolving around the fundamental extremal principle in variational analysis and its analytic counterpart known as the subdifferential variational principle.

#### Article information

Source
Taiwanese J. Math., Volume 12, Number 9 (2008), 2569-2592.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405196

Digital Object Identifier
doi:10.11650/twjm/1500405196

Mathematical Reviews number (MathSciNet)
MR2479072

Zentralblatt MATH identifier
1169.49024

#### Citation

Bao, Truong Q.; Mordukhovich, Boris S.; Gupta, Pankaj. SUBOPTIMALITY CONDITIONS FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS. Taiwanese J. Math. 12 (2008), no. 9, 2569--2592. doi:10.11650/twjm/1500405196. https://projecteuclid.org/euclid.twjm/1500405196

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