Set Relations and Weak Minimal Solutions for Nonconvex Set Optimization Problems with Applications

Zhang, Chuang-liang; Huang, Ning

doi:10.1007/s10957-021-01913-z

Cited by 5 publications

(2 citation statements)

References 32 publications

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“…Sach and Le [18] obtained an Ekeland's principle in the sense of upper set order and lower set order relations. Zhang and Huang [19] presented an Ekeland's principle in terms of strict lower set order relation. An Ekeland's variational principle with respect to weighted set relations defined by Gerstewitz's function was discussed in [4].…”

Section: Introductionmentioning

confidence: 99%

Ekeland’s variational principle with a scalarization type weighted set order relation

2023

J. Nonlinear Var. Anal.

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In this paper, a weighted set order relation given by the oriented distance function is introduced, which does not need any convexity and is applicable even the ordering cone has an empty interior. The Ekeland's variational principle, Caristi's fixed point theorem, and Takahashi's minimization theorem associated with the introduced weighted set order relation are constructed, and the equivalences among them are deduced. As an application, the existence of solutions to a set optimization problem is examined to verify the validity of the results obtained.

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Section: Introductionmentioning

confidence: 99%

Ekeland’s variational principle with a scalarization type weighted set order relation

2023

J. Nonlinear Var. Anal.

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“…The research on setvalued optimization has achieved fruitful results (see [6,9,13,15]). The study of set optimization has been investigated by some authors (see [11,12,14,21,23]). Kuroiwa [14] considered the criteria of solutions of set optimization, showed some examples with respect to the criteria, introduced some type of semicontinuities for set-valued maps, and showed existence theorems of solutions.…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions for set optimization with an order cone that has nonempty quasirelative interiors

Zhao

Huang

2022

J Inequal Appl

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In a real normed linear space, when the quasirelative interior is not empty, a class of order relation is introduced with Minkowski difference. Two classes of nonlinear functions are introduced, and their properties are discussed. A class of approximately efficient solutions and approximate weakly efficient solutions are introduced for set optimization. With nonlinear functions, optimality conditions are established for approximate solutions. Some examples are given to illustrate our main results.

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An unified scalarization and Ekeland’s variational principle for partial set order

Han,

2024

Comp. Appl. Math.

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Set Relations and Weak Minimal Solutions for Nonconvex Set Optimization Problems with Applications

Cited by 5 publications

References 32 publications

Ekeland’s variational principle with a scalarization type weighted set order relation

Ekeland’s variational principle with a scalarization type weighted set order relation

Approximate solutions for set optimization with an order cone that has nonempty quasirelative interiors

An unified scalarization and Ekeland’s variational principle for partial set order

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