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On Calmness of the Argmin Mapping in Parametric Optimization Problems

Diethard Klatte (diethard.klatte***at***business.uzh.ch)
Bernd Kummer (kummer***at***math.hu-berlin.de)

Abstract: Recently, Canovas et. al. (2013) 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 programs, optimal value function, optimal set mapping

Category 1: Nonlinear Optimization

Category 2: Infinite Dimensional Optimization (Semi-infinite Programming )

Category 3: Complementarity and Variational Inequalities

Citation: Accepted version, published in J. Optim. Theory Appl. (2015) 165: 708-719. The final version is available at link.springer.com

Download: [PDF]

Entry Submitted: 02/19/2014
Entry Accepted: 02/19/2014
Entry Last Modified: 09/27/2017

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