Displaying similar documents to “Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities”

Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm

Lateef O. Jolaoso, Oluwatosin T. Mewomo (2020)

Commentationes Mathematicae Universitatis Carolinae

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This paper presents an inertial iterative algorithm for approximating a common solution of split equalities of generalized mixed equilibrium problem, monotone variational inclusion problem, variational inequality problem and common fixed point problem in real Hilbert spaces. The algorithm is designed in such a way that it does not require prior knowledge of the norms of the bounded linear operators. We prove a strong convergence theorem under some mild conditions of the control sequences...

The Perturbed Generalized Tikhonov's Algorithm

Alexandre, P. (1999)

Serdica Mathematical Journal

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We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.

An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators

A. Renaud, G. Cohen (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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To find a zero of a maximal monotone operator, an extension of the Auxiliary Problem Principle to nonsymmetric auxiliary operators is proposed. The main convergence result supposes a relationship between the main operator and the nonsymmetric component of the auxiliary operator. When applied to the particular case of convex-concave functions, this result implies the convergence of the parallel version of the Arrow-Hurwicz algorithm under the assumptions of Lipschitz and partial...

Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

Muhammad Aqeel Ahmad Khan (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the...

Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Brohe, M., Tossings, P. (2000)

Serdica Mathematical Journal

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Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of...

Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities

Christina Jager (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and...

Note on the paper: interior proximal method for variational inequalities on non-polyhedral sets

Alexander Kaplan, Rainer Tichatschke (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we clarify that the interior proximal method developed in [6] (vol. 27 of this journal) for solving variational inequalities with monotone operators converges under essentially weaker conditions concerning the functions describing the "feasible" set as well as the operator of the variational inequality.