Journal
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
Volume 180, Issue 3, Pages 1087-1097Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-018-1438-7
Keywords
Pessimistic bilevel problem; Inner regularization; Viscosity solution
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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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