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Smooth approximations to nonlinear complementarity problems. (English) Zbl 0879.90177

Summary: It is well known that a nonlinear complementarity problem (NCP) can be formulated as a system of nonsmooth equations. C. Chen and O. L. Mangasarian [Comput. Optim. Appl. 5, No. 2, 97-138 (1996; Zbl 0859.90112)] proposed a class of parametric smooth functions by twice integrating a probability density function. As a result, the nonsmooth equations can be approximated by smooth equations. This paper refines the smooth functions proposed by Chen and Mangasarian and investigates their structural properties. The refinement allows us to establish the existence, uniqueness, and limiting properties of the trajectory defined by the solutions of these smooth equation approximations. In addition, global error bounds for the NCP with a uniform P-function are obtained.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Citations:

Zbl 0859.90112
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