Journal
OPTIMIZATION
Volume 68, Issue 2-3, Pages 433-455Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331934.2018.1543294
Keywords
Optimistic and pessimistic bilevel programming; two-level value functions; variational analysis; generalized differentiation; optimality conditions
Funding
- Deutsche Forschungsgemeinschaft [DE 650/10-1]
- USA National Science Foundation [DMS-1512846]
- USA Air Force Office of Scientific Research [15RT0462]
- RUDN University Program 5-100
- Engineering and Physical Sciences Research Council (EPSRC) [EP/P022553/1]
- EPSRC [EP/P022553/1] Funding Source: UKRI
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The authors' paper in Dempe et al. [Necessary optimality conditions in pessimistic bilevel programming. Optimization. 2014;63:505-533], was the first one to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal value function introduced and analysed in Dempe et al. [Sensitivity analysis for two-level value functions with applications to bilevel programming. SIAM J. Optim. 22 (2012), 1309-1343], for the case of optimistic bilevel programs. One of the basic assumptions in both of these papers is that the functions involved in the problems are at least continuously differentiable. Motivated by the fact that many real-world applications of optimization involve functions that are non-differentiable at some points of their domain, the main goal of the current paper is to extend the two-level value function approach by deriving new necessary optimality conditions for both optimistic and pessimistic versions in bilevel programming with non-smooth data.
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