Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/15079
Title: Lower-order penalty methods for mathematical programs with complementarity constraints
Authors: Yang, XQ 
Huang, XX
Keywords: B-stationary point
Convergence
Mathematical program with complementarity constraints
Optimality condition
Penalty function
Issue Date: 2004
Publisher: Taylor & Francis
Source: Optimization methods and software, 2004, v. 19, no. 6, p. 693-720 How to cite?
Journal: Optimization methods and software 
Abstract: In this article, a smooth mathematical program with complementarity constraints (MPCC) is reformulated as a non-smooth constrained optimization problem by using the Fischer-Burmeister function. A lower-order penalty method is applied to transform the resulted constrained optimization problem into unconstrained optimization problems. Lower-order penalty functions may not be locally Lipschitz. However, they require weaker conditions to guarantee an exact penalization property than the classical l1 penalty functions. We derive optimality conditions for the penalty problems using a smooth approximate variational principle, and establish that the limit point of a sequence of points that satisfy the second-order necessary optimality conditions of penalty problems is a strongly stationary point (hence a B-stationary point) of the original MPCC if the limit point is feasible to MPCC, and a linear independence constraint qualification for MPCC and an upper level strict complementarity condition hold at the limit point. Furthermore, the limit point also satisfies a second-order necessary condition of MPCC. Numerical examples are presented to demonstrate and compare the effectiveness of the proposed methods.
URI: http://hdl.handle.net/10397/15079
ISSN: 1055-6788
DOI: 10.1080/1055678041001697659
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