A NEW REGULARIZATION METHOD FOR MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS WITH STRONG CONVERGENCE PROPERTIES

作者：Kanzow Christian^*; Schwartz Alexandra

来源：SIAM Journal on Optimization, 2013, 23(2): 770-798.

DOI：10.1137/100802487

• mathematical programs with complementarity constraints
• regularization method
• global convergence
• M-stationarity
• strong stationarity
• constraint qualifications

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.

• 出版日期2013