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'''Mathematical programming with equilibrium constraints (MPEC)''' is the study of
[[constrained optimization]] problems where the constraints include [[variational inequalities]] or [[complementarity theory|complementarities]]. MPEC is related to the [[Stackelberg game]].

MPEC is used in the study of [[engineering design]], [[economic equilibrium]], and [[multilevel games]].

MPEC is difficult to deal with because its [[feasible region]] is not necessarily [[Convex set|convex]] or even [[Connected space|connected]].

==References==
<references/>
* Z.-Q. Luo, J.-S. Pang and D. Ralph: ''Mathematical Programs with Equilibrium Constraints''. Cambridge University Press, 1996, {{isbn|0-521-57290-8}}.
* B. Baumrucker, J. Renfro, L. T. Biegler, MPEC problem formulations and solution strategies with chemical engineering applications, Computers & Chemical Engineering, 32 (12) (2008) 2903-2913.
* A. U. Raghunathan, M. S. Diaz, L. T. Biegler, An MPEC formulation for dynamic optimization of distillation operations, Computers & Chemical Engineering, 28 (10) (2004) 2037-2052.

==External links==
* [http://apmonitor.com/wiki/index.php/Apps/MpecExamples MPEC examples] such as SIGN, ABS, MIN, and MAX
* [http://apmonitor.com/me575/index.php/Main/LogicalConditions Formulating logical statements] as continuously differentiable nonlinear programming problems

[[Category:Mathematical optimization]]

{{mathapplied-stub}}

Mathematical programming with equilibrium constraints - Revision history

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