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.