A Sequential Bundle Method for Solving a MPEC Problem

Xia Zunquan; Shen Jie; Pang Liping

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A Sequential Bundle Method for Solving a MPEC Problem

Xia Zunquan 1 * #,Shen Jie 2,Pang Liping 3

1.Department of Applied Mathematics, Dalian University of Technology

2.Department of Applied Mathematics, Dalian University of Technology；Liaoning Normal University

3.Department of Applied Mathematics- Dalian University of Technology

*Correspondence author

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Funding: 国家自然科学基金、教育部博士点基金（No.20020141013；10471015）

Opened online:19 October 2005

Accepted by: none

Citation: Xia Zunquan,Shen Jie ,Pang Liping.A Sequential Bundle Method for Solving a MPEC Problem[OL]. [19 October 2005] http://en.paper.edu.cn/en_releasepaper/content/3308

In this paper we consider a convex MPEC problem with a nondifferentiable convex objective function and constraints separable in two variable vectors whose second variable vector belongs to the set of optimal solutions of the constraint problem. A sequential bundle method for dealing with this kind of problem is presented. It is constructed by combining a proximal bundle method due to Hintermuller (2001) and a descent proximal level bundle method due to Brannlund, Kiwiel and Lindberg (1995). The first bundle method is used to provide a starting point at the beginning of each iteration of the sequential iterate process and the second one is used to find an (approximate) optimal solution of the constraint problem at each iteration of the sequential iterate process. The convergence analysis given in the last section shows that under some conditions the algorithm presented can terminate at an approximate solution in finite steps according to a given tolerance error.

Keywords:Nonlinear programming, nonsmooth optimization, MPEC (Mathematical Programs with Equilibrium Constraints) problem, Bundle method, level bundle method, proximal bundle method

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