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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.

##### MSC:
 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming
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