Convergence of optimal values of quadratic penalty problems for mathematical programs with complementarity constraints

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July 2006, 2(3): 287-296. doi: 10.3934/jimo.2006.2.287

Convergence of optimal values of quadratic penalty problems for mathematical programs with complementarity constraints

X. X. Huang ^1, , D. Li ^2, and Xiaoqi Yang ^3,

1.	School of Management, Fudan University, Shanghai 200433, China
2.	Department of Systems Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong, China
3.	Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China

Received May 2005 Revised February 2006 Published July 2006

Abstract
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In this note, a mathematical program with complementarity constraints (MPCC) is reformulated as a nonsmooth constrained mathematical program via the Fischer-Burmeister function. Quadratic penalty functions are used to treat this nonsmooth constrained program. We investigate necessary and sufficient conditions that guarantee the convergence of optimal values of unconstrained penalized problems to the optimal value of the original MPCC.

Keywords: convergence., optimal value, penalty function, Mathematical program with complementarity constraints.

Mathematics Subject Classification: Primary: 90C30; Secondary: 90C46, 90C3.

Citation: X. X. Huang, D. Li, Xiaoqi Yang. Convergence of optimal values of quadratic penalty problems for mathematical programs with complementarity constraints. Journal of Industrial & Management Optimization, 2006, 2 (3) : 287-296. doi: 10.3934/jimo.2006.2.287

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