On Approximate Stationary Points of the Regularized Mathematical Program with Complementarity Constraints

Jean-Pierre Dussault (), Mounir Haddou (), Abdeslam Kadrani () and Tangi Migot ()
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Jean-Pierre Dussault: Université de Sherbrooke
Mounir Haddou: Univ Rennes, INSA Rennes, CNRS, IRMAR - UMR 6625
Abdeslam Kadrani: INSEA, Laboratoire SI2M Rabat-Instituts
Tangi Migot: University of Guelph

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 2, No 8, 504-522

Abstract: Abstract We discuss the convergence of regularization methods for mathematical programs with complementarity constraints with approximate sequence of stationary points. It is now well accepted in the literature that, under some tailored constraint qualification, the genuine necessary optimality condition for this problem is the M-stationarity condition. It has been pointed out, (Kanzow and Schwartz in Math Oper Res 40(2):253–275. 2015), that relaxation methods with approximate stationary points fail to ensure convergence to M-stationary points. We define a new strong approximate stationarity concept, and we prove that a sequence of strong approximate stationary points always converges to an M-stationary solution. We also prove under weak assumptions the existence of strong approximate stationary points in the neighborhood of an M-stationary solution.

Keywords: Nonlinear programming; MPCC; Regularization methods; Constraint qualification; Optimization model with complementarity constraints; 90C30; 90C33; 49M37; 65K05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01706-w

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