On the vectorial Ekeland's variational principle and minimal points in product spaces

Göpfert, Alfred; Tammer, Christiane; Zălinescu, Constantin

doi:10.1016/s0362-546x(98)00255-7

Cited by 121 publications

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“…In [3], Chen and Huang discussed a vector Ekeland variational principle for set-valued mappings by using Ekeland variational principle of a real function and a nonlinear scalarization function. In [10], using the concept of cone extension and the Mordukhovich coderivative, Ha [9]. In [14], Li et al proved a general Ekeland variational principle for a half distance vector valued function (see Theorem 2.1) by using Dancs-Hegedus-Medvegyev Theorem (see [5]).…”

Section: Introductionmentioning

confidence: 99%

On Ekeland's Variational Principle for Set-Valued Mappings

Zhang

2007

Acta Mathematicae Applicatae Sinica, English Series

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Section: Introductionmentioning

confidence: 99%

On Ekeland's Variational Principle for Set-Valued Mappings

Zhang

2007

Acta Mathematicae Applicatae Sinica, English Series

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“…On the other hand, the second conclusion is applicable to the vector variational principle in Goepfert, Tammer, and Zȃlinescu [25]; see, for instance, Turinici [55]. It also works for the results in Sect.…”

Section: (I) Any Maximal/variational Principle (Mp) With (Dc) H) (Mp)mentioning

confidence: 70%

“…Further, the topological vector space realm is discussed in the papers by Nemeth [43] and Turinici [54]. A "product" type version of these results is to be found in Goepfert, Tammer, and Zȃlinescu [25]; see also Isac [32]. Now, the natural question to be posed is that of these extensions being or not effective.…”

Section: Introductionmentioning

confidence: 99%

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Maximal and Variational Principles in Vector Spaces

Turinici

2015

Computation, Cryptography, and Network Security

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In Sect. 1, a separable type extension of Ekeland's variational principle (J Math Anal Appl 47:324-353, 1974) is given, in the realm of ordered convergence spaces. The connections with a related statement in Khanh (Bull Acad Pol Sci (Math) 37: [33][34][35][36][37][38][39] 1989) are then discussed. In Sect. 2, the Brezis-Browder ordering principle (Adv Math 21:355-364, 1976) is used to establish a lot of maximality results in triangular structures due to Pasicki (Nonlinear Anal 74:5678-5684, 2011). Finally, in Sect. 3, some technical aspects of the variational principle due to Bao and Mordukhovich (Control Cyb 36:531-562, 2007) are being analyzed. Further, an extension of this result is proposed, by means of a pseudometric maximal principle in Turinici (Note Mat 28:33-41, 2008).

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“…Very general versions of the maximal point lemma (in spaces X ×Z, X a complete metric space, Z a locally convex Hausdorff space) can be found for example in [11], [12]. Note that it is also possible to derive Theorem 3 from Fang's Theorem 3.2 in [9].…”

Section: Theorem 6 Theorem 3 and Theorem 2 Are Mutually Equivalentmentioning

confidence: 99%

Phelps’ lemma, Danes’ drop theorem and Ekeland’s principle in locally convex spaces

Hamel

2003

Proc. Amer. Math. Soc.

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Abstract. A generalization of Phelps' lemma to locally convex spaces is proven, applying its well-known Banach space version. We show the equivalence of this theorem, Ekeland's principle and Danes' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto efficiency theorem due to Isac. This solves a problem, concerning the drop theorem, proposed by G. Isac in 1997.We show that a different formulation of Ekeland's principle in locally convex spaces, using a family of topology generating seminorms as perturbation functions rather than a single (in general discontinuous) Minkowski functional, turns out to be equivalent to the original version.

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On the vectorial Ekeland's variational principle and minimal points in product spaces

Cited by 121 publications

References 0 publications

On Ekeland's Variational Principle for Set-Valued Mappings

On Ekeland's Variational Principle for Set-Valued Mappings

Maximal and Variational Principles in Vector Spaces

Phelps’ lemma, Danes’ drop theorem and Ekeland’s principle in locally convex spaces

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