New Constrained Optimization Reformulation of Complementarity Problems

A. Fischer
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A. Fischer: Technical University of Dresden

Journal of Optimization Theory and Applications, 1998, vol. 97, issue 1, No 7, 105-117

Abstract: Abstract We suggest a reformulation of the complementarity problem CP(F) as a minimization problem with nonnegativity constraints. This reformulation is based on a particular unconstrained minimization reformulation of CP(F) introduced by Geiger and Kanzow as well as Facchinei and Soares. This allows us to use nonnegativity constraints for all the variables or only a subset of the variables on which the function F depends. Appropriate regularity conditions ensure that a stationary point of the new reformulation is a solution of the complementarity problem. In particular, stationary points with negative components can be avoided in contrast to the reformulation as unconstrained minimization problem. This advantage will be demonstrated for a class of complementarity problems which arise when the Karush–Kuhn–Tucker conditions of a convex inequality constrained optimization problem are considered.

Keywords: Complementarity problems; reformulation as constrained minimization problems; stationary points; convex optimization (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1022627217515

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