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• W2083546784 abstract "Mathematical programs with equilibrium (or complementarity) constraints (MPECs) form a difficult class of optimization problems. The feasible set has a very special structure and violates most of the standard constraint qualifications. Therefore, one typically applies specialized algorithms in order to solve MPECs. One very prominent class of specialized algorithms are the regularization (or relaxation) methods. The first regularization method for MPECs is due to Scholtes [SIAM J. Optim., 11 (2001), pp. 918--936], but in the meantime, there exist a number of different regularization schemes which try to relax the difficult constraints in different ways. However, almost all regularization methods converge to C-stationary points only, which is a very weak stationarity concept. An exception is a recent method by Kadrani, Dussault, and Benchakroun [SIAM J. Optim., 20 (2009), pp. 78--103], whose limit points are shown to be M-stationary. Here we provide a new regularization method which also converges to M-stationary points. The assumptions to prove this result are, in principle, significantly weaker than for all other relaxation schemes. Furthermore, our relaxed problem has a much more favorable geometric shape than the one proposed by Kadrani, Dussault, and Benchakroun." @default.
• W2083546784 created "2016-06-24" @default.
• W2083546784 creator A5056161700 @default.
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• W2083546784 date "2013-01-01" @default.
• W2083546784 modified "2023-10-05" @default.
• W2083546784 title "A New Regularization Method for Mathematical Programs with Complementarity Constraints with Strong Convergence Properties" @default.
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• W2083546784 doi "https://doi.org/10.1137/100802487" @default.
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