A smoothing method for mathematical programs with equilibrium constraints. (English) Zbl 0959.65079

The authors propose an algorithm for solving optimization problems whose constraints include a strongly monotone variational inequality. Their idea is to reformulate the considered problem as a one-level nonsmoothly constrained optimization problem \((P)\) by using the Karush-Kuhn-Tucker conditions for the variational inequality.
Next, they introduce a sequence \((P_{\mu^k})\) of smooth, regular one-level problems which progressively approximate the nonsmooth problem \((P)\). It is proved that the sequence of solutions of the problems \((P_{\mu^k})\) is contained in a compact set and that each of its limit points is a solution of the original problem.
Furthermore, it is shown that the sequence of stationary points of the problems \((P_{\mu^k})\) is also contained in a compact set and that its limit points furnish strongly \(C\)-stationary points of the original problem.


65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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