On the convergence properties of modified augmented Lagrangian methods for mathematical programming with complementarity constraints

Authors:
H. Z. Luo;X. L. Sun;Y. F. Xu;H. X. Wu
Affiliations:
Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433 and Department of Applied Mathematics, Zhejiang University of Technology, Hang ...;Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433;Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433;Department of Mathematics, Hangzhou Dianzi University, Hangzhou, Zhejiang, People's Republic of China 310018
Venue:
Journal of Global Optimization
Year:
2010

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Abstract

In this paper, we present new convergence results of augmented Lagrangian methods for mathematical programs with complementarity constraints (MPCC). Modified augmented Lagrangian methods based on four different algorithmic strategies are considered for the constrained nonconvex optimization reformulation of MPCC. We show that the convergence to a global optimal solution of the problem can be ensured without requiring the boundedness condition of the multipliers.