Set-valued increasing-along-rays maps and well-posed set-valued star-shaped optimization

Hu, Rong; Fang, Ya-Ping

doi:10.1016/j.jmaa.2006.09.073

Cited by 8 publications

(3 citation statements)

References 27 publications

(60 reference statements)

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“…Well-posedness of optimization problems was first studied by Tykhonov [1] in 1966. Since then, the notions of well-posedness have been extended to different kinds of optimization problems (see [2,3,4,5,6,7]). In the book edited by Lucchetti and Revalski [8], Loridan gave a survey on some theoretical results of well-posedness, approximate solutions and variational principles in vector optimization.…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for set optimization problems

Zhang

Teo

2009

Nonlinear Analysis: Theory, Methods & Applications

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In this paper, three kinds of well-posedness for set optimization are first introduced. By virtue of a generalized Gerstewitz's function, the equivalent relations between the three kinds of well-posedness and the well-posedness of three kinds of scalar optimization problems are established, respectively. Then, sufficient and necessary conditions of well-posedness for set optimization problems are obtained by using a generalized forcing function, respectively. Finally, various criteria and characterizations of well-posedness are given for set optimization problems.

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Section: Introductionmentioning

confidence: 99%

Well-posedness for set optimization problems

Zhang

Teo

2009

Nonlinear Analysis: Theory, Methods & Applications

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“…Some authors have extended and studied the notion of well-posedness for setvalued vector optimization problems (see e.g., Hu and Fang 2007;Fang et al 2007;Xu and Zhang 2011). The notion of well-posedness for set optimization problems was first given by Zhang et al (2009).…”

Section: Introductionmentioning

confidence: 99%

Pointwise well-posedness and scalarization in set optimization

Khoshkhabar-amiranloo

Khorram

2015

Math Meth Oper Res

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In this paper, some notions of pointwise well-posedness for set optimization problems are introduced. Some relationships among these notions are established. Using a new nonlinear scalarization function, pointwise well-posed set optimization problems are characterized by means of a family of Tykhonov well-posed scalar optimization problems. Also, three classes of well-posed set optimization problems are identified.

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“…Well-posedness of optimization problems was first studied by Tykhonov [1] in 1966. Since then, the notion of wellposedness has been extended to different kinds of optimization problems (see [2][3][4][5]). In the book edited by Lucchetti and Revalski [6], Loridan gave a survey on some theoretical results of well-posedness, approximate solutions, and variational principles in vector optimization.…”

Section: Introductionmentioning

confidence: 99%