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Diethard Klatte, On calmness of the optimal value function

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DOI: 10.23952/asvao.5.2023.2.09
Volume 5, Issue 2, 1 August 2023, Pages 253-264


Abstract. The paper is devoted to the calmness from below/from above for the optimal value function \varphi of parametric optimization problems, where we are specifically interested in perturbed semi-infinite programs. A main intention is to revisit classical results and to derive refinements of them. In particular, we show in the context of semi-infinite optimization that calmness from below for \varphi holds under quasi-convexity of the data functions and compactness of the solution set, which extends results on the lower semicontinuity of \varphi. Illustrative examples are given, which demonstrate the significance of the imposed assumptions even in the case of linear and quadratic programs.


How to Cite this Article:
D. Klatte, On calmness of the optimal value function, Appl. Set-Valued Anal. Optim. 5 (2023), 253-264.