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On the implicit programming approach in a class of mathematical programs with equilibrium constraints

Outrata J. V., Cervinka M.

Control and Cybernetics

2009

Vol. 38, no 4B

1557-1574

In the paper we analyze the influence of implicit programming hypothesis and presence of state constraints on first order optimality conditions to mathematical programs with equilibrium constraints. In the absence of state constraints, we derive sharp stationarity conditions, provided the strong regularity condition holds. In the second part of the paper we suggest an exact penalization of state constraints and test the behavior of standard bundle trust region algorithm on academic examples.

Radiality and semismoothness

Jourani A.

Control and Cybernetics

2007

Vol. 36, no 3

669-680

We provide sufficient conditions for radiality and semismoothness. In general Banach spaces, we show that calmness ensures Dini-radiality as well as Dini-convexity of solution set to inequality systems. In finite dimensional spaces, we introduce the concept of Clarke-radiality and semismoothness of order m and show that each subanalytic set satisfies these properties. Similar properties are obtained for locally Lipschitzian subanalytic functions.