-stable functions are continuous

Bednařík, Dušan; Pastor, Karel

doi:10.1016/j.na.2008.03.011

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ò ø óò 1º1

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Cited by 20 publications

(16 citation statements)

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“…The properties of −stable at some point functions were studied e. g. in [1,4,5,6,7,8,11,12,14,15,28,29,30] for both scalar and vector functions. Among the others, the sufficient second-order optimality condition for problem (1) was stated indepedently in [14] and [8] in terms of −stable at some point functions.…”

Section: 1mentioning

confidence: 99%

Necessary conditions for vector optimization in infinite dimension

Dvorská¹,

Pastor²

2016

Kybernetika

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Section: 1mentioning

confidence: 99%

Necessary conditions for vector optimization in infinite dimension

Dvorská¹,

Pastor²

2016

Kybernetika

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“…in [BP2,BP3,BP4,BP5,BP6,G,GG,LX]. In [G] and [BP4,BP6,GG] the notion of -stable at a point scalar function was broadened to a vector function by two formally different ways.…”

Section: ò ø óò 1ºmentioning

confidence: 99%

On comparison of ℓ-stable vector optimization results

Dvorská

Pastor

2014

Mathematica Slovaca

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ABSTRACT. Two papers with similar optimality conditions were published by I. Ginchev, and by D. Bednařík and K. Pastor independently in Nonlinear Analysis in 2011. We compare these results. We also show the equivalence of two definitions of -stability of vector functions. Moreover, we generalize another result given by I. Ginchev and V. I. Ivanov [J. Math. Anal. Appl. 340 (2008), 646-657] and compare it with the previously mentioned optimality conditions.

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“…The properties of scalar or vector functions that are -stable at some point functions and their applications in optimization were studied e. g. in [1,2,3,4,5,6,7,8,9,12,13,15,16,24,25,28,30,31]. Let us remind that a second-order sufficient optimality condition for the constrained scalar problem for -stable at some point function in terms of Dini derivatives was introduced in [28].…”

Section: Introductionmentioning

confidence: 99%