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Elastic-Mode Algorithms for Mathematical Programs with Equilibrium Constraints: Global Convergence and Stationarity Properties

Mihai Anitescu (anitescu***at***mcs.anl.gov)
Paul Tseng (tseng***at***math.washington.edu)
Stephen J. Wright (swright***at***cs.wisc.edu)

Abstract: 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.

Keywords: Nonlinear programming, equilibrium constraints, complementarity constraints, elastic-mode formulation, strong stationarity, C-stationarity, M-stationarity

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Complementarity and Variational Inequalities

Citation: Preprint ANL/MCS P1242-0405, MCS Division, Argonne National Laboratory

Download: [PDF]

Entry Submitted: 04/16/2005
Entry Accepted: 04/16/2005
Entry Last Modified: 11/03/2006

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