Relationships between the oriented distance functional and a nonlinear separation functional

Li, G.H.; Li, S.J.; You, Manxue

doi:10.1016/j.jmaa.2018.06.046

Cited by 9 publications

(2 citation statements)

References 15 publications

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“…Here, we obtain complete characterizations of the monotonicity of ∆ A via free disposal set. Therefore, our results improve and generalize those of [27]. (ii) Gao and Yang [12] have established the monotonicity properties of the oriented distance function under the assumption that the associated set is closed, convex and co-radiant.…”

Section: Remark 1 (I)supporting

confidence: 76%

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Some properties of nonconvex oriented distance function and applications to vector optimization problems

Tang¹,

Gao²

2021

Journal of Industrial &Amp; Management Optimization

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In this paper, we study some interesting properties of nonconvex oriented distance function. In particular, we present complete characterizations of monotonicity properties of oriented distance function. Moreover, the Clark subdifferentials of nonconvex oriented distance function are explored in the solid case. As applications, fuzzy necessary optimality conditions for approximate solutions to vector optimization problems are provided.

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Section: Remark 1 (I)supporting

confidence: 76%

“…Remark 4. (i) The monotonicity of ∆ A was also discussed by Li et al [27] in terms of the recession cone A ∞ , where…”

Section: Remark 1 (I)mentioning

confidence: 85%

Some properties of nonconvex oriented distance function and applications to vector optimization problems

Tang¹,

Gao²

2021

Journal of Industrial &Amp; Management Optimization

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Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization

et al. 2021

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A Unified Characterization of Nonlinear Scalarizing Functionals in Optimization

Bouza¹,

Quintana²,

Tammer³

2019

Vietnam J. Math.

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Over the years, several classes of scalarization techniques in optimization have been introduced and employed in deriving separation theorems, optimality conditions and algorithms. In this paper, we study the relationships between some of those classes in the sense of inclusion. We focus on three types of scalarizing functionals defined by Hiriart-Urruty, Drummond and Svaiter, Gerstewitz. We completely determine their relationships. In particular, it is shown that the class of the functionals by Gerstewitz is minimal in this sense. Furthermore, we define a new (and larger) class of scalarizing functionals that are not necessarily convex, but rather quasidifferentiable and positively homogeneous. We show that our results are connected with some of the set relations in set optimization.

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Relationships between the oriented distance functional and a nonlinear separation functional

Cited by 9 publications

References 15 publications

Some properties of nonconvex oriented distance function and applications to vector optimization problems

Some properties of nonconvex oriented distance function and applications to vector optimization problems

Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization

A Unified Characterization of Nonlinear Scalarizing Functionals in Optimization

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