A Smooth Variational Principle for Vector Optimization Problems

Göpfert, Alfred; Henkel, E.-Chr.; Tammer, Christiane

doi:10.1007/978-3-642-46823-0_12

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Level Sets Minimality Boundedness Lower Semicontinuity1

Introduction1

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2017

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Cited by 2 publications

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“…for some bounded subset M ⊂ Y . Obviously, f is level C-bounded at x if it is C-(lower) bounded [26]: f (X) ⊂ M + C for some bounded subset M ⊂ Y ; cf. [29,37,38].…”

Section: Level Sets Minimality Boundedness Lower Semicontinuitymentioning

confidence: 99%

“…Along with various scalarization techniques, generalized vector metrics have been used [15,17,24]. Some authors have considered directional and more general set perturbations [16,18,21,23,[25][26][27][28][29][30][31][32]. Using the latter approach, Bednarczuk and Zagrodny [31] obtained recently an extension of the Borwein-Preiss variational principle to vector-valued functions.…”

Section: Introductionmentioning

confidence: 99%

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Borwein–Preiss vector variational principle

2017

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This article extends to the vector setting the results of our previous work Kruger et al. (2015) which refined and slightly strengthened the metric space version of the Borwein-Preiss variational principle due to Li and Shi, J. Math. Anal. Appl. 246(1), 308-319 (2000). We introduce and characterize two seemingly new natural concepts of ǫ-minimality, one of them dependant on the chosen element in the ordering cone and the fixed "gauge-type" function.

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“…for some bounded subset M ⊂ Y . Obviously, f is level C-bounded at x if it is C-(lower) bounded [26]: f (X) ⊂ M + C for some bounded subset M ⊂ Y ; cf. [29,37,38].…”

Section: Level Sets Minimality Boundedness Lower Semicontinuitymentioning

confidence: 99%