A smoothing method for mathematical programs with equilibrium constraints

A smoothing method for mathematical programs with equilibrium constraints

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Article ID: iaor20001813
Country: Germany
Volume: 85
Issue: 1
Start Page Number: 107
End Page Number: 134
Publication Date: Jan 1999
Journal: Mathematical Programming
Authors: , ,
Abstract:

The mathematical program with equilibrium constraints (MPEC) is an optimization problem with variational inequality constraints. MPEC problems include bilevel programming problems as a particular case and have a wide range of applications. MPEC problems with strongly monotone variational inequalities are considered in this paper. They are transformed into an equivalent one-level nonsmooth optimization problem. Then, a sequence of smooth, regular problems that progressively approximate the nonsmooth problem and that can be solved by standard available software for constrained optimization is introduced. It is shown that the solutions (stationary points) of the approximate problems converge to a solution (stationary point) of the original MPEC problem. Numerical results showing viability of the approach are reported.

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