Journal
OPTIMIZATION METHODS & SOFTWARE
Volume 27, Issue 3, Pages 483-512Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10556788.2010.535170
Keywords
mathematical programmes with equilibrium constraints; mathematical programmes with vanishing constraints; regularization method; global convergence
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Funding
- international doctorate programme 'Identification, Optimization, and Control with Applications in Modern Technologies' within the Elite-Network of Bavaria
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Mathematical programmes with equilibrium or vanishing constraints (MPECs or MPVCs) are both known to be difficult optimization problems which typically violate all standard constraint qualifications. A number of methods try to exploit the particular structure of MPECs and MPVCs in order to overcome these difficulties. In a recent paper by Steffensen and Ulbrich (S. Steffensen and M. Ulbrich, A new regularization scheme for mathematical programs with equilibrium constraints, SIAM J. Optim. 2010.), this was done for MPECs by a local regularization idea that may be viewed as a modification of the popular global regularization technique by Scholtes (S. Scholtes, Convergence properties of a regularization scheme for mathematical programs with complementarity constraints, SIAM J. Optim. 11 (2001), pp. 918-936.). The aim of this paper is twofold. First, we improve the convergence theory from (S. Steffensen and M. Ulbrich, A new regularization scheme for mathematical programs with equilibrium constraints, SIAM J. Optim. 2010.) in the MPEC setting, and second we translate this local regularization idea to MPVCs and obtain a new solution method for this class of optimization problems for which several convergence results are given.
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