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2 Control and Cybernetics

2 2009

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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.

Exact penalization of pointwise constraints for optimal control problems

Casas E.

Control and Cybernetics

2009

Vol. 38, no 4A

1131-1150

In this paper we consider a control problem governed by a semilinear elliptic equation with pointwise control and state constraints. We analyze the existence of an exact penalization of the state constraints. In particular, we prove that the first and second order optimality conditions imply the existence of such a penalization. Finally, we prove some extra regularity of the strict local minima of the control problem, assuming the existence of an exact penalization for them.