Displaying similar documents to “Approximating solutions of split equality of some nonlinear optimization problems using an inertial algorithm”

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...

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...

Modified golden ratio algorithms for pseudomonotone equilibrium problems and variational inequalities

Lulu Yin, Hongwei Liu, Jun Yang (2022)

Applications of Mathematics

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We propose a modification of the golden ratio algorithm for solving pseudomonotone equilibrium problems with a Lipschitz-type condition in Hilbert spaces. A new non-monotone stepsize rule is used in the method. Without such an additional condition, the theorem of weak convergence is proved. Furthermore, with strongly pseudomonotone condition, the $R$-linear convergence rate of the method is established. The results obtained are applied to a variational inequality problem, and the convergence...

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.

Kaczmarz algorithm with relaxation in Hilbert space

Ryszard Szwarc, Grzegorz Świderski (2013)

Studia Mathematica

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We study the relaxed Kaczmarz algorithm in Hilbert space. The connection with the non-relaxed algorithm is examined. In particular we give sufficient conditions when relaxation leads to the convergence of the algorithm independently of the relaxation coefficients.

A modified algorithm for the strict feasibility problem

D. Benterki, B. Merikhi (2010)

RAIRO - Operations Research

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In this note, we present a slight modification of an algorithm for the strict feasibility problem. This modification reduces the number of iterations.

Dynamic contact problems in bone neoplasm analyses and the primal-dual active set (PDAS) method

Nedoma, Jiří

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In the contribution growths of the neoplasms (benign and malignant tumors and cysts), located in a system of loaded bones, will be simulated. The main goal of the contribution is to present the useful methods and efficient algorithms for their solutions. Because the geometry of the system of loaded and possible fractured bones with enlarged neoplasms changes in time, the corresponding mathematical models of tumor's and cyst's evolutions lead to the coupled free boundary problems and...