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Mihai Anitescu (anitescumcs.anl.gov) Abstract: We prove that any accumulation point of an elastic mode approach, applied to the optimization of a mixed P variational inequality, that approximately solves the relaxed subproblems is a Cstationary point of the problem of optimizing a parametric mixed P variational inequality. If, in addition, the accumulation point satises the MPCCLICQ constraint qualication and if the solutions of the subproblem satisfy approximate secondorder sucient conditions, then the limiting point is an Mstationary point. Moreover, if the accumulation point satises the upperlevel strict complementarity condition, the accumulation point will be a strongly stationary point. If we assume that the penalty function associated with the feasible set of the mathematical program with complementarity constraints has bounded level sets and if the objective function is bounded below, we show that the algorithm will produce bounded iterates and will therefore have at least one accumulation point. We prove that the obstacle problem satises our assumptions for both a rigid and a deformable obstacle. The theoretical conclusions are validated by several numerical examples. Keywords: MPCC, global convergence, complementarity constraints, nonlinear programming, Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Complementarity and Variational Inequalities Category 3: Applications  Science and Engineering (Mechanical Engineering ) Citation: Preprint ANL/MCSP11430404, Argonne National Laboratory, Argonne, Illinois, April 2004. Download: [PDF] Entry Submitted: 08/03/2004 Modify/Update this entry  
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