Inner Regularizations and Viscosity Solutions for Pessimistic Bilevel Optimization Problems

M. Beatrice Lignola () and Jacqueline Morgan
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M. Beatrice Lignola: Università di Napoli Federico II

CSEF Working Papers from Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy

Abstract: Pessimistic bilevel optimization problems are not guaranteed to have a solution even when restricted classes of data are involved. Thus, we propose a concept of viscosity solution which can satisfactory obviate the lack of optimal solutions since it allows to achieve in appropriate conditions the security value. Differently from the viscosity solution concept for optimization problems, introduced by H. Attouch in 1996 and defined through a viscosity function that aims to regularize the objective function, viscosity solutions for pessimistic bilevel optimization problems are defined through regularization families of the solutions map to the lower level optimization These families are termed "inner regularizations" since they approach the optimal solutions map from the inside. First, we investigate several classical regularizations of parametric minimum problems giving sufficient conditions for getting inner regularizations; then, we establish existence results for the corresponding viscosity solutions.

Date: 2016-03-30
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Published in Journal of Optimization Theory and Applications, 2017, 173(1), pp. 183-202

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Journal Article: Inner Regularizations and Viscosity Solutions for Pessimistic Bilevel Optimization Problems (2017)
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