Mathematical programs with complementarity constraints: Convergence properties of a smoothing method

• 成果类型: Article
• 署名作者: Bouza, Gemayqzel; Still, Georg
• 署名单位: Universidad de la Habana
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1060.0245
• 发表日期: 2007
• 页码: 467-483
• 关键词: regularization; sensitivity; optimality; schemes

摘要

In this paper, optimization problems P with complementarity constraints are considered. Characterizations for local minimizers (x) over bar of P of Orders 1 and 2 are presented. We analyze a parametric smoothing approach for solving these programs in which P is replaced by a perturbed problem P-tau depending on a (small) parameter tau. We are interested in the convergence behavior of the feasible set F-tau and the convergence of the solutions (x) over bar (7) of P-tau for tau -> 0. In particular, it is shown that, under generic assumptions, the solutions (x) over bar (tau) are unique and converge to a solution (x) over bar of P with a rate O(root tau). Moreover, the convergence for the Hausdorff distance d(F-tau, F) between the feasible sets of P-tau and P is of order O(root tau).