Results 131 to 140 of about 465 (165)

Vector Ekeland Variational Principle

2000
In this paper the well-known Ekeland variational principle is generalized to the case where vector-valued functions are involved. Namely, vector Ekeland variational principle is studied. In particular, the epsilon vector minimum point of a vector optimization problem is investigated via vector Ekeland variational principle.
Shen Jie Li, Xiao Qi Yang, Guang-ya Chen
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Versions of Ekeland’s variational principle involving set perturbations

Journal of Global Optimization, 2012
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Phan Quoc Khanh, Dinh Ngoc Quy
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Ekeland’s Variational Principle for Functions Unbounded from below

The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 2020
This paper is devoted to variational principles of nonlinear analysis for functions whose domain is a generalized metric space. A modification of the Ekeland variational principle for functions unbounded from below is obtained. For a wide class of differentiable functions not necessarily bounded below, it is shown that there exists a minimizing ...
Sengupta, R., Zhukovskiy, S.
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General Ekeland's Variational Principle for Set-Valued Mappings

Journal of Optimization Theory and Applications, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, G. Y., Huang, X. X., Hou, S. H.
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Ekeland's ε-variational principle for set-valued mappings

Mathematical Methods of Operations Research, 1998
In this paper, we introduce the concept of approximate solutions for set-valued mappings and provide a sufficient condition for the existence of approximate solutions of set-valued mappings. We obtain an approximate variational principle for set-valued mappings.
Guang-Ya Chen, X. X. Huang
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A general vectorial Ekeland’s variational principle with a P-distance

Acta Mathematica Sinica, English Series, 2013
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Qiu, Jing Hui, He, Fei
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Sequentially lower complete spaces and Ekeland’s variational principle

Acta Mathematica Sinica, English Series, 2015
The main result of this paper establishes a version of the vectorial Ekeland variational principle for sequentially lower monotone maps in the framework of sequentially lower complete spaces. This abstract result enables the authors to deduce as corollaries a vectorial Caristi fixed point theorem and a vectorial Takahashi nonconvex minimization theorem.
He, Fei, Qiu, Jing-Hui
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Equivalent formulations of Ekeland's variational principle

Nonlinear Analysis: Theory, Methods & Applications, 2003
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Vectorial Ekeland Variational Principles: A Hybrid Approach

2015
This paper proposes a hybrid approach in establishing vectorial versions of Ekeland’s variational principle. It bases on both the nonlinear scalarization functional in Tammer (Gerth) and Weidner’s nonconvex separation theorem [14] from a scalarization approach and Bao and Mordukhovich’s iterative scheme in [5] from a variational approach.
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On Ekeland’s Variational Principle for Pareto Minima of Set-Valued Mappings

Journal of Optimization Theory and Applications, 2011
In [J. Glob. Optim. 49, No. 3, 381--396 (2011; Zbl 1216.49018)] and [Nonlinear Anal. 73, No. 7, 2245--2259 (2010; Zbl 1194.58014)] the authors proposed a definition of a weak \(\tau \)-function. In the present paper, using this concept of weak \(\tau\)-function they get relaxed lower semicontinuity properties of a set-valued mapping and, imposing these
Phan Quoc Khanh, Dinh Ngoc Quy
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