Solving normalized stationary points of a class of equilibrium problem with equilibrium constraints

Peiyu Li

doi:10.3934/jimo.2017065

Article Contents

2018, Volume 14, Issue 2: 637-646. Doi: 10.3934/jimo.2017065

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Solving normalized stationary points of a class of equilibrium problem with equilibrium constraints

Peiyu Li^,

School of Sciences, Southwest Petroleum University, Xindu Avenue No.8, Xindu District, Chengdu City, 610500, China

* Corresponding author: Peiyu li
* Corresponding author: Peiyu li

Received: February 29, 2016

Early access: May 2017

Published: March 2018

The author is supported by NSFC grant 11501476

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Abstract

This paper focuses on solving normalized stationary points of a class of equilibrium problem with equilibrium constraints (EPEC). We show that, under some kind of separability assumption, normalized C-/M-/S-stationary points of EPEC are actually C-/M-/S-stationary points of an associated mathematical program with equilibrium constraints (MPEC), which implies that we can solve MPEC to obtain normalized stationary points of EPEC. In addition, we demonstrate the proposed approach on competition of manufacturers for similar products in the same city.

Keywords:

Equilibrium problem with equilibrium constraints,
mathematical program with equilibrium constraints,
stationary point.

Mathematics Subject Classification: Primary: 90B50, 90C33; Secondary: 65K10.

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