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Journal of Convex Analysis 16 (2009), No. 1, 261--276
Copyright Heldermann Verlag 2009

Existence of Exact Penalty and its Stability for Inequality-Constrained Optimization Problems

Alexander J. Zaslavski
Department of Mathematics, Technion - Israel Institute of Technology, 32000 Haifa, Israel

We use the penalty approach in order to study a large class of inequality-constrained minimization problems in Banach spaces. A penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. In this paper we show that the generalized exact penalty property is stable under perturbations of cost functions, constraint functions and the right-hand side of constraints.

Keywords: Approximate solution, Ekeland's variational principle, minimization problem, penalty function.

MSC: 49M30, 90C30

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