Calmness of the Argmin Mapping in Linear Semi-Infinite Optimization

Cánovas, M. J.; Hantoute, Abderrahim; Parra, J.; Toledo, Francisco Javier Castro

doi:10.1007/s10957-013-0371-z

Cited by 15 publications

(26 citation statements)

References 21 publications

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“…al. [1], which gave the impetus for our studies and has been devoted to the following special setting of problem (1) with parameter space T = R n × C(I, R):…”

Section: Notation and Preliminariesmentioning

confidence: 99%

“…We will focus here to calmness of this multifunction. For the definition of calmness and other Lipschitz-type concepts we refer to Section 2, for more details or recent surveys on calmness see, e.g., [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“…al. [1], where such a characterization was given for the special class of linear semi-infinite programs under canonical perturbations. It is shown there that, under the Slater CQ, the argmin mapping is calm if and only if some associated linear semi-infinite inequality system is calm.…”

Section: Introductionmentioning

confidence: 99%

“…Note that the authors of [1] essentially used the structure of the linear semiinfinite setting, the special parametrization, and some subdifferential approach to calmness by Azé and Corvellec [13]. In contrast to it, we will apply both classical tools from parametric optimization (cf., e.g., [14][15][16]) and a basic intersection theorem for calm multifunctions [3,14].…”

Section: Introductionmentioning

confidence: 99%

“…In Section 3, it will be shown that in our abstract setting (cf. (1) below), the calmness of the argmin mapping at some reference point is implied by the calmness of the mentioned auxiliary mapping, provided that the Slater CQ is replaced, e.g., by the Aubin property of the feasible set mapping at the reference point (which is equivalent to the Slater CQ in the framework of [1]). It is worth noting that the proofs do not use any structure of the feasible set and go only back to classical tools in parametric optimization from the 1980ies.…”

Section: Introductionmentioning

confidence: 99%

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On Calmness of the Argmin Mapping in Parametric Optimization Problems

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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 semiinfinite 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. 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.

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“…al. [1], which gave the impetus for our studies and has been devoted to the following special setting of problem (1) with parameter space T = R n × C(I, R):…”

Section: Notation and Preliminariesmentioning

confidence: 99%