Mathematical programs with equilibrium constraints

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Mathematical Programs with Equilibrium Constraints (MPEC) is a special subject in nonlinear programming (NLP). MPEC is also called mathematical programming with complementarity Constraints. MPEC problem can be considered as a combination of NLP and mixed complementarity programming. The basic form of MPEC is:

Minimize \quad f(\mathbf{x},\mathbf{y})
Subject to
\mathbf{g}(\mathbf{x},\mathbf{y}) \in \mathbf{Z}
\mathbf{F}(\mathbf{x},\mathbf{y}) \le \mathbf{0} \perp (\mathbf{v-y}) \ge \mathbf{0}
\mathbf{y} \in \mathbf{C}(\mathbf{x}), \forall \mathbf{v} \in \mathbf{C}(\mathbf{x})

where Z is the fesible region for the upper level problem and C(x) is the feasible region for the lower level problem.

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