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Title: Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
Authors: Liu, X. 
Sun, J. 
Keywords: Global convergence
Interior-point methods
Mathematical programming with equilibrium constraints
Stationary point
Issue Date: 2004
Citation: Liu, X., Sun, J. (2004). Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints. Mathematical Programming 101 (1) : 231-261. ScholarBank@NUS Repository.
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 under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). 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 point with certain 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. © Springer-Verlag 2004.
Source Title: Mathematical Programming
ISSN: 00255610
DOI: 10.1007/s10107-004-0543-6
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