Mathematical programming with equilibrium constraints (MPEC) is the study of
constrained optimization

Optimization (mathematics)

In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....

 problems where the constraints include variational inequalities or complementarities

Complementarity theory

A complementarity problem is a type of mathematical optimization problem. It is the problem of optimizing a function of two vector variables subject to certain requirements which include: that the inner product of the two variables must equal zero, i.e.  = 0...

. MPEC is related to the Stackelberg game.

MPEC is used in the study of engineering design, economic equilibrium

Economic equilibrium

In economics, economic equilibrium is a state of the world where economic forces are balanced and in the absence of external influences the values of economic variables will not change. It is the point at which quantity demanded and quantity supplied are equal...

 and multilevel games.

MPEC is difficult to deal with because its feasible region is not necessarily convex or even connected.