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The penalty interior point method fails to converge for mathematical programs with equilibrium constraints. University of Dundee Report NA208 (2002)

by S Leyffer
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Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints

by Xinwei Liu, Jie Sun - Industrial Engineering & Management Sciences, Northwestern University , 2005
"... Abstract. Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier proble ..."
Abstract - Cited by 12 (0 self) - Add to MetaCart
Abstract. Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). Under certain general assumptions, the algorithm can always find some point with strong or weak stationarity. In particular, it is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a certain point with weak stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point. Key words: Global convergence, interior-point methods, mathematical programming with equilibrium constraints, stationary point
The National Science Foundation
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