On certain conditions for the existence of solutions of equilibrium problems

Iusem, Alfredo N.; Kassay, G.; Sosa, Wilfredo

doi:10.1007/s10107-007-0125-5

Cited by 137 publications

(83 citation statements)

References 13 publications

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“…The characterizations of solution set of various equilibrium problem had been studied by many authors (see, [5,6,7,8,10,12]). Here we assume that S 1 and S 2 are nonempty, closed and convex with S 1 S 2 = ∅.…”

Section: Resultsmentioning

confidence: 99%

A composition projection method for feasibility problems and applications to equilibrium problems

Chen¹,

Liou²,

Khan³

et al. 2016

J. Nonlinear Sci. Appl.

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In this article, we propose a composition projection algorithm for solving feasibility problem in Hilbert space. The convergence of the proposed algorithm are established by using gap vector which does not involve the nonempty intersection assumption. Moreover, we provide the sufficient and necessary condition for the convergence of the proposed method. As an application, we investigate the split feasibility equilibrium problem.

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Section: Resultsmentioning

confidence: 99%

A composition projection method for feasibility problems and applications to equilibrium problems

Chen¹,

Liou²,

Khan³

et al. 2016

J. Nonlinear Sci. Appl.

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“…Observe that conditions related to A1(h, X ) have been already exploited by many authors and can be found, for instance, in [3][4][5][6]19,20]. Now, we are able to show a technical procedure in order to check nonemptiness of the solution set of SCM.…”

Section: For Allmentioning

confidence: 94%

“…Theorem 8 Under our general assumptions of problem (18), i.e., assuming that X is a nonempty, closed and convex polyhedral set, the convex dual problem generated from the perturbation function φ, as defined in (19), is the following:…”

Section: Lemma 4 S N × S M Is a Dual Conjugate Space Of φ As Defined Inmentioning

confidence: 99%

Semi-continuous quadratic optimization: existence conditions and duality scheme

2015

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In this work, we study the class of problems called semi-continuous optimization, which contains constrained minimization (maximization) problems with lower (upper) semicontinuous objective functions. We show some existence conditions for solutions based on asymptotic techniques, as well as a duality scheme based on the Fenchel-Moreau conjugation specifically applied to semi-continuous problems. Promising results are obtained, when we apply this scheme to minimize quadratic functions (whose Hessians can be symmetric indefinite) over nonempty, closed and convex polyhedral sets.

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“…Conditions related to assumptions H1 or H2 can be found, for instance, in [1], [2], [4], [12], [13], [14] and references therein.…”

Section: (6) S(h) Is Nonempty Convex and Compactmentioning

confidence: 99%

“…The notion of pseudo-convexity for functions in the setting of real vectorial spaces (without topological structure) appears in [13] as follows, given a function h : R n → R ∪ {+∞}, we say that f is pseudo-convex if for all (x, y) ∈ R n × R n and all t ∈]0, 1[:…”

Section: Theorem 410 Given Ep(fk) If F Satisfies F0 and H Definedmentioning

confidence: 99%

From weierstrass to ky fan theorems and existence results on Optimization and Equilibrium Problems

Sosa

2013

Pesqui. Oper.

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ABSTRACT.In this work, we study coerciveness notions and their implications to existence conditions. We start with the presentation of classical ideas of coerciveness in the framework of Optimization Theory, and, then, using a classical technical result, introduced by Ky Fan in 1961, we extend these ideas first to Optimization Problems and then to Equilibrium Problems. We point out the importance of related conditions to the introduced coerciveness notion in order to obtain existence results for Equilibrium Problems, without using monotonicity or generalized monotonicity assumptions.

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On certain conditions for the existence of solutions of equilibrium problems

Cited by 137 publications

References 13 publications

A composition projection method for feasibility problems and applications to equilibrium problems

A composition projection method for feasibility problems and applications to equilibrium problems

Semi-continuous quadratic optimization: existence conditions and duality scheme

From weierstrass to ky fan theorems and existence results on Optimization and Equilibrium Problems

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