Special Issue "Symmetry in Nonlinear Functional Analysis and Optimization Theory"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 30 April 2020.

Special Issue Editor

Prof. Sun Young Cho
E-Mail Website
Guest Editor
Department of Mathematics, Gyeongsang National University, Jinju 660-701, Korea
Interests: nonlinear functional analysis; optimization theory; complementary problems; differential equation; equilibrium problems; monotone operators; convex feasibility problems; split feasibility problems; machine learning

Special Issue Information

Dear Colleagues,

Nonlinear Functional Analysis and Optimization Theory are two closed related two research fields in applied mathematics. A lot of problems such as differential equations and integral equations in nonlinear analysis, can be solved via optimization methods. In particular, fixed/zero-point problems nonlinear operators are under the spotlight of mathematicians working on optimization theory. Recently, a number of optimization methods, such as, projection-like methods, have been investigated for solving various nonlinear equations. Many important applications have been carried out in engineering fields, such as, transportation, economics, medicine, and machine learning.

In this Special Issue, we will focus on high-quality research on nonlinear functional analysis and optimization theory, in particular complementary problems, differential equation, integral equations, equilibrium problems, monotone operators, fixed/zero points, convex feasibility problems, split feasibility problems and their applications to the real world.

Please note that all submitted papers must be within the general scope of the Symmetry journal.

Prof. Sun Young Cho
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complementary problems
  • differential equation
  • equilibrium problems
  • monotone operators
  • convex feasibility problems
  • split feasibility problems
  • machine learning

Published Papers (3 papers)

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Research

Open AccessArticle
On a General Extragradient Implicit Method and Its Applications to Optimization
Symmetry 2020, 12(1), 124; https://doi.org/10.3390/sym12010124 - 08 Jan 2020
Abstract
Let X be a Banach space with both q-uniformly smooth and uniformly convex structures. This article introduces and considers a general extragradient implicit method for solving a general system of variational inequalities (GSVI) with the constraints of a common fixed point problem [...] Read more.
Let X be a Banach space with both q-uniformly smooth and uniformly convex structures. This article introduces and considers a general extragradient implicit method for solving a general system of variational inequalities (GSVI) with the constraints of a common fixed point problem (CFPP) of a countable family of nonlinear mappings { S n } n = 0 and a monotone variational inclusion, zero-point, problem. Here, the constraints are symmetrical and the general extragradient implicit method is based on Korpelevich’s extragradient method, implicit viscosity approximation method, Mann’s iteration method, and the W-mappings constructed by { S n } n = 0 . Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)
Open AccessArticle
Parallel Tseng’s Extragradient Methods for Solving Systems of Variational Inequalities on Hadamard Manifolds
Symmetry 2020, 12(1), 43; https://doi.org/10.3390/sym12010043 - 24 Dec 2019
Abstract
The aim of this article is to study two efficient parallel algorithms for obtaining a solution to a system of monotone variational inequalities (SVI) on Hadamard manifolds. The parallel algorithms are inspired by Tseng’s extragradient techniques with new step sizes, which are established [...] Read more.
The aim of this article is to study two efficient parallel algorithms for obtaining a solution to a system of monotone variational inequalities (SVI) on Hadamard manifolds. The parallel algorithms are inspired by Tseng’s extragradient techniques with new step sizes, which are established without the knowledge of the Lipschitz constants of the operators and line-search. Under the monotonicity assumptions regarding the underlying vector fields, one proves that the sequences generated by the methods converge to a solution of the monotone SVI whenever it exists. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)
Open AccessArticle
Hybrid Algorithms for Variational Inequalities Involving a Strict Pseudocontraction
Symmetry 2019, 11(12), 1502; https://doi.org/10.3390/sym11121502 - 11 Dec 2019
Abstract
In a real Hilbert space, we investigate the Tseng’s extragradient algorithms with hybrid adaptive step-sizes for treating a Lipschitzian pseudomonotone variational inequality problem and a strict pseudocontraction fixed-point problem, which are symmetry. By imposing some appropriate weak assumptions on parameters, we obtain a [...] Read more.
In a real Hilbert space, we investigate the Tseng’s extragradient algorithms with hybrid adaptive step-sizes for treating a Lipschitzian pseudomonotone variational inequality problem and a strict pseudocontraction fixed-point problem, which are symmetry. By imposing some appropriate weak assumptions on parameters, we obtain a norm solution of the problems, which solves a certain hierarchical variational inequality. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory)
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