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Stationary Points of Bound Constrained Minimization Reformulations of Complementarity Problems

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Abstract

We consider two merit functions which can be used for solving the nonlinear complementarity problem via nonnegatively constrained minimization. One of the functions is the restricted implicit Lagrangian (Refs. 1–3), and the other appears to be new. We study the conditions under which a stationary point of the minimization problem is guaranteed to be a solution of the underlying complementarity problem. It appears that, for both formulations, the same regularity condition is needed. This condition is closely related to the one used in Ref. 4 for unrestricted implicit Lagrangian. Some new sufficient conditions are also given.

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  1. Institute de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

    M. V. Solodov (Assistant Professor)

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  1. M. V. Solodov
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Solodov, M.V. Stationary Points of Bound Constrained Minimization Reformulations of Complementarity Problems. Journal of Optimization Theory and Applications 94, 449–467 (1997). https://doi.org/10.1023/A:1022695931376

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