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 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 enter ...
,
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 polytop ...
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 examplessuch as SIGN, ABS, MIN, and MAX
Formulating logical statementsas continuously differentiable nonlinear programming problems
Mathematical optimization
{{mathapplied-stub