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 ob ...

problems where the constraints include variational inequalities or complementarities. MPEC is related to the Stackelberg game. MPEC is used in the study of engineering design,

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 Multilevel or multi-level may refer to: * A hierarchy A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at th ...

. MPEC is difficult to deal with because its feasible region 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 polytop ...

or even connected.

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