On Calmness of the Argmin Mapping in Parametric Optimization Problems

Diethard Klatte () and Bernd Kummer ()
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Diethard Klatte: Universität Zürich
Bernd Kummer: Humboldt-Universität zu Berlin

Journal of Optimization Theory and Applications, 2015, vol. 165, issue 3, No 2, 708-719

Abstract: Abstract Recently, Cánovas et al. presented an interesting result: the argmin mapping of a linear semi-infinite program under canonical perturbations is calm if and only if some associated linear semi-infinite inequality system is calm. Using classical tools from parametric optimization, we show that the if-direction of this condition holds in a much more general framework of optimization models, while the opposite direction may fail in the general case. In applications to special classes of problems, we apply a more recent result on the intersection of calm multifunctions.

Keywords: Calm multifunctions; Parametric optimization problems; Optimal value function; Optimal set mapping; Perturbed nonlinear programs; Convex semi-infinite programs; 49J53; 49K40; 90C31; 90C34 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-014-0643-2

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