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 (mathematics), inequality involving a Functional (mathematics), functional, which has to be Inequality (mathematics)#Solving Inequalities, solved for all possible values of a given Variable ( ...
or
complementarities. MPEC is related to the
Stackelberg game.
MPEC is used in the study of
engineering design
The engineering design process, also known as the engineering method, 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 repeat ...
,
economic equilibrium
In economics, economic equilibrium is a situation in which the economic forces of supply and demand are balanced, meaning that economic variables will no longer change.
Market equilibrium in this case is a condition where a market price is es ...
, and
multilevel games.
MPEC is difficult to deal with because its
feasible region
In mathematical optimization and computer science, a feasible region, feasible set, 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, ...
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 examplessuch as SIGN, ABS, MIN, and MAX
Formulating logical statementsas continuously differentiable nonlinear programming problems
Mathematical optimization
{{mathapplied-stub