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

constrained optimization In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The obj ...

problems where the constraints include

variational inequalities In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initial ...

or complementarities. MPEC is related to the Stackelberg game. MPEC is used in the study of

engineering design The engineering design process is a common series of steps that engineers use in creating functional products and processes. The process is highly iterative - parts of the process often need to be repeated many times before another can be entere ...

economic equilibrium In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the ( equilibrium) values of economic variables will not change. For example, in the st ...

, and multilevel games. MPEC is difficult to deal with because its

feasible region In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potent ...

is not necessarily

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytope ...

or even

connected Connected may refer to: Film and television * ''Connected'' (2008 film), a Hong Kong remake of the American movie ''Cellular'' * '' Connected: An Autoblogography About Love, Death & Technology'', a 2011 documentary film * ''Connected'' (2015 TV ...

References

* Z.-Q. Luo, J.-S. Pang and D. Ralph: ''Mathematical Programs with Equilibrium Constraints''. Cambridge University Press, 1996, . * 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

MPEC examples
such as SIGN, ABS, MIN, and MAX
Formulating logical statements
as continuously differentiable nonlinear programming problems Mathematical optimization {{mathapplied-stub