Results 141 to 150 of about 343 (158)

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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On Ha’s version of set-valued Ekeland’s variational principle

Acta Mathematica Sinica, English Series, 2011
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On the Ekeland variational principle

2011
For proper lower semicontinuous functionals bounded from below which do not increase upon polarization, an improved version of Ekeland’s variational principle can be formulated in Banach spaces, which provides almost symmetric ...
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An unified scalarization and Ekeland’s variational principle for partial set order

Computational and Applied Mathematics
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Wenyan Han, Guolin Yu
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On a complement to Ekeland's variational principle

1997
We give a sufficient condition to a closed convex hull of the set of the Ekeland's points of a certain lower semicontinuous function defined on a real Banach space X coincides with X.
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