Elastic-mode algorithms for mathematical programs with equilibrium constraints: global convergence and stationarity properties

• 成果类型: Article
• 署名作者: Anitescu, Mihai; Tseng, Paul; Wright, Stephen J.
• 署名单位: United States Department of Energy (DOE); Argonne National Laboratory; University of Washington; University of Washington Seattle; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0005-4
• 发表日期: 2007
• 页码: 337-371
• 关键词: optimization problems; regularization; optimality; point

摘要

The elastic-mode formulation of the problem of minimizing a nonlinear function subject to equilibrium constraints has appealing local properties in that, for a finite value of the penalty parameter, local solutions satisfying first- and second-order necessary optimality conditions for the original problem are also first- and second-order points of the elastic-mode formulation. Here we study global convergence properties of methods based on this formulation, which involve generating an (exact or inexact) first- or second-order point of the formulation, for nondecreasing values of the penalty parameter. Under certain regularity conditions on the active constraints, we establish finite or asymptotic convergence to points having a certain stationarity property (such as strong stationarity, M-stationarity, or C-stationarity). Numerical experience with these approaches is discussed. In particular, our analysis and the numerical evidence show that exact complementarity can be achieved finitely even when the elastic-mode formulation is solved inexactly.