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Optimization problems with equilibrium constraints and their numerical solution

Michal Kocvara (kocvara***at***am.uni-erlangen.de)
Jiri Outrata (outrata***at***utia.cas.cz)

Abstract: We consider a class of optimization problems with a generalized equation among the constraints. This class covers several problem types like MPEC (Mathematical Programs with Equilibrium Constraints) and MPCC (Mathematical Programs with Complementarity Constraints). We briefly review techniques used for numerical solution of these problems: penalty methods, nonlinear programming (NLP) techniques and Implicit Programming approach (ImP). We further present a new theoretical framework for the ImP technique that is particularly useful in case of difficult equilibria. Finally, three numerical examples are presented: an MPEC that can be solved by ImP but can hardly be formulated as a nonlinear program, an MPCC that cannot be solved by ImP and finally an MPEC solvable by both, ImP and NLP techniques. In the last example we compare the efficiency of the two approaches.

Keywords: Mathematical Programs with Equilibrium Constraints

Category 1: Other Topics (Other )

Category 2: Complementarity and Variational Inequalities

Category 3: Nonlinear Optimization (Other )

Citation: Research Report 298, Institute of Applied Mathematics, University of Erlangen, 2003.

Download: [Postscript][PDF]

Entry Submitted: 02/03/2003
Entry Accepted: 02/03/2003
Entry Last Modified: 02/04/2003

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