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Mathematical programming with equilibrium constraints
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<p>Mathematical programming with equilibrium constraints (MPEC) is the study of <a href="/facts/Constrained_optimization/tJuCmQ4b">constrained optimization</a> problems where the constraints include <a href="/facts/Variational_inequalities/p3Hy60WS">variational inequalities</a> or <a href="/facts/Complementarity_theory/WYSSukXu">complementarities</a>. MPEC is related to the <a href="/facts/Stackelberg_game/cpr1PFfw">Stackelberg game</a>. </p><p>MPEC is used in the study of <a href="/facts/Engineering_design/heCF3wFo">engineering design</a>, <a href="/facts/Economic_equilibrium/lFTmEyUS">economic equilibrium</a>, and multilevel games. </p><p>MPEC is difficult to deal with because its <a href="/facts/Feasible_region/cJUKNCmM">feasible region</a> is not necessarily <a href="/facts/Convex_set/vdAuJRJl">convex</a> or even <a href="/facts/Connected_space/5CUTxfoA">connected</a>. </p> <ul><li>Z.-Q. Luo, J.-S. Pang and D. Ralph: <i>Mathematical Programs with Equilibrium Constraints</i>. Cambridge University Press, 1996, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-521-57290-8.</li> <li>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.</li> <li>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.</li></ul>