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Further on Inner Regularizations in Bilevel Optimization

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Abstract

A crucial difficulty in pessimistic bilevel optimization is the possible lack of existence of exact solutions since marginal functions of the sup type may fail to be lower semicontinuous. So, to overcome this drawback, we have introduced, in Lignola and Morgan (J Optim Theory Appl 173(1):183–202, 2017), suitable inner regularizations of the lower level optimization problem together with relative viscosity solutions for the pessimistic bilevel problem. Here, we continue this research by considering new inner regularizations of the lower level optimization problem, which not necessarily satisfy the constraints but that are close to them, and by deriving an existence result of related viscosity solutions to the pessimistic bilevel problem.

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Authors and Affiliations

  1. Department of Mathematics and Applications R. Caccioppoli, University of Naples Federico II, Napoli, Via Claudio 21, 80125, Naples, Italy

    M. Beatrice Lignola

  2. Department of Economics and Statistics and Center for Studies in Economics and Finance, University of Naples Federico II, Napoli, Via Cinthia, 80126, Naples, Italy

    Jacqueline Morgan

Authors
  1. M. Beatrice Lignola
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  2. Jacqueline Morgan
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Correspondence to Jacqueline Morgan.

Additional information

Communicated by Alexander Mitsos.

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Lignola, M.B., Morgan, J. Further on Inner Regularizations in Bilevel Optimization. J Optim Theory Appl 180, 1087–1097 (2019). https://doi.org/10.1007/s10957-018-1438-7

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  • DOI: https://doi.org/10.1007/s10957-018-1438-7

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