New Constraint Qualifications for Mathematical Programs with Equilibrium Constraints via Variational Analysis

Abstract

In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. Compared with the usual way of formulating MPEC through a KKT condition, this formulation has the advantage that it does not involve extra multipliers as new variables, and it usually requires weaker assumptions on the problem data. Using the so-called first-order sufficient condition for metric subregularity, we derive verifiable sufficient conditions for the metric subregularity of the involved set-valued mapping, or equivalently the calmness of the perturbed generalized equation mapping.

Keywords

  1. mathematical programs with equilibrium constraints
  2. constraint qualification
  3. metric subregularity
  4. calmness

MSC codes

  1. 49J53
  2. 90C30
  3. 90C33
  4. 90C46

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Information & Authors

Information

Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization
Pages: 842 - 865
ISSN (online): 1095-7189

History

Submitted: 9 August 2016
Accepted: 18 January 2017
Published online: 9 May 2017

Keywords

  1. mathematical programs with equilibrium constraints
  2. constraint qualification
  3. metric subregularity
  4. calmness

MSC codes

  1. 49J53
  2. 90C30
  3. 90C33
  4. 90C46

Authors

Affiliations

Funding Information

Austrian Science Fund https://doi.org/10.13039/501100002428 : P26132-N25, P29190-N32
Natural Sciences and Engineering Research Council of Canada https://doi.org/10.13039/501100000038

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