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Symmetry
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Symmetry and Asymmetry in Nonlinear Analysis, Optimization and Related Topics
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Symmetry and Asymmetry in Nonlinear Analysis, Optimization and Related Topics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 5303

Special Issue Editors

Prof. Dr. Wei-Shih Du

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Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis; fixed point theory and its applications; variational principles and inequalities; optimization theory; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals
Dr. Alexander Zaslavski

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Guest Editor
Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel
Interests: variational and optimal control problems on unbounded domains; optimization theory and related topics; infinite products of operators and their applications
Special Issues, Collections and Topics in MDPI journals
Dr. Huaping Huang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404020, China
Interests: nonlinear functional analysis; complex analysis and differential equation theory; theory of fixed point in metric spaces and abstract metric spaces
Special Issues, Collections and Topics in MDPI journals
Dr. Narin Petrot

E-Mail Website
Guest Editor
1. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2. Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Interests: optimization algorithms and its applications

Special Issue Information

Dear Colleagues,

For more than a century, nonlinear analysis has had widespread and significant applications in many fields at the core of many branches of pure and applied mathematics, including functional analysis, fixed point theory, variational analysis, convex analysis, nonlinear ordinary and partial differential equations, nonsmooth analysis, critical point theory, nonlinear optimization, fractional calculus and its applications, probability and statistics, dynamical system theory, mathematical economics, data mining, signal processing, and control theory. Additionally, there have been further applications in modern science, including in physics, biological engineering, electronic networks, electromagnetic theory, financial economics, and so on. It is known that there are plenty of problems that occur in the real world that have been solved using different optimization algorithms and techniques via a mathematical model. For the past six decades, the construction and processing of artificial intelligence (AI) models has been one of the hottest research topics. AI researchers have come up with a number of powerful optimization techniques and tools to optimize AI models. In fact, various feasible optimization algorithms have been used as powerful tools in the optimization process of artificial intelligence.

This Special Issue will focus on the new originality of nonlinear analysis, optimization, and related topics in integrating basic science into the real world, covering  symmetry and asymmetry. This Special Issue provides a platform for researchers to present their novel findings, innovative methodologies, and practical applications that contribute to the advancement of these interconnected domains. We cordially and earnestly invite researchers to contribute their original and high-quality research papers which will inspire advances in nonlinear analysis, optimization, and related topics with applications. Potential topics include, but are not limited to:

  • Symmetry and asymmetry in fixed point theory with applications;
  • Symmetry and asymmetry in fractional integro-differential equations;
  • Symmetry and asymmetry in nonlinear dynamical systems;
  • Symmetry and asymmetry in image and signal processing;
  • Symmetry and asymmetry in inverse and ill-posed problems;
  • Symmetry and asymmetry in optimization;
  • Nonsmooth analysis;
  • Critical point theory;
  • Convex analysis and mathematical inequalities;
  • Intelligence computation;
  • Set-valued analysis;
  • Nonlinear functional analysis;
  • Computational intelligence;
  • Machine learning;
  • Data analytics.

Prof. Dr. Wei-Shih Du
Dr. Alexander Zaslavski
Dr. Huaping Huang
Dr. Narin Petrot
Guest Editors

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 submissions that pass pre-check are 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 2400 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

  • fixed point theory with applications
  • fractional integro-differential equations
  • nonlinear dynamical systems
  • inverse and ill-posed problems
  • optimization
  • nonsmooth analysis
  • critical point theory
  • convex analysis
  • mathematical inequalities
  • intelligence computation
  • set-valued analysis
  • nonlinear functional analysis
  • computational intelligence
  • machine learning
  • data analytics

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

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Research

14 pages, 2628 KiB  
Article
Fed-RHLP: Enhancing Federated Learning with Random High-Local Performance Client Selection for Improved Convergence and Accuracy
by Pramote Sittijuk and Kreangsak Tamee
Symmetry 2024, 16(9), 1181; https://doi.org/10.3390/sym16091181 - 9 Sep 2024
Viewed by 941
Abstract
We introduce the random high-local performance client selection strategy, termed Fed-RHLP. This approach allows opportunities for higher-performance clients to contribute more significantly by updating and sharing their local models for global aggregation. Nevertheless, it also enables lower-performance clients to participate collaboratively based on [...] Read more.
We introduce the random high-local performance client selection strategy, termed Fed-RHLP. This approach allows opportunities for higher-performance clients to contribute more significantly by updating and sharing their local models for global aggregation. Nevertheless, it also enables lower-performance clients to participate collaboratively based on their proportional representation determined by the probability of their local performance on the roulette wheel (RW). Improving symmetry in federated learning involves IID Data: symmetry is naturally present, making model updates easier to aggregate and Non-IID Data: asymmetries can impact performance and fairness. Solutions include data balancing, adaptive algorithms, and robust aggregation methods. Fed-RHLP enhances federated learning by allowing lower-performance clients to contribute based on their proportional representation, which is determined by their local performance. This fosters inclusivity and collaboration in both IID and Non-IID scenarios. In this work, through experiments, we demonstrate that Fed-RHLP offers accelerated convergence speed and improved accuracy in aggregating the final global model, effectively mitigating challenges posed by both IID and Non-IID Data distribution scenarios. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Analysis, Optimization and Related Topics)
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17 pages, 521 KiB  
Article
New Convergence Theorems for Pseudomonotone Variational Inequality on Hadamard Manifolds
by Zhaoli Ma and Lin Wang
Symmetry 2023, 15(11), 2085; https://doi.org/10.3390/sym15112085 - 19 Nov 2023
Viewed by 1135
Abstract
In this paper, we propose an efficient viscosity type subgradient extragradient algorithm for solving pseudomonotone variational inequality on Hadamard manifolds which is of symmetrical characteristic. Under suitable conditions, we obtain the convergence of the iteration sequence generated by the proposed algorithm to a [...] Read more.
In this paper, we propose an efficient viscosity type subgradient extragradient algorithm for solving pseudomonotone variational inequality on Hadamard manifolds which is of symmetrical characteristic. Under suitable conditions, we obtain the convergence of the iteration sequence generated by the proposed algorithm to a solution of a pseudomonotone variational inequality on Hadamard manifolds. We also employ our main result to solve a constrained convex minimization problem and present a numerical experiment to illustrate the asymptotic behavior of the algorithm. Our results develop and improve some recent results. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Analysis, Optimization and Related Topics)
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Figure 1

18 pages, 341 KiB  
Article
Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function
by Yue-Wu Li, Feng Qi and Wei-Shih Du
Symmetry 2023, 15(9), 1686; https://doi.org/10.3390/sym15091686 - 1 Sep 2023
Cited by 7 | Viewed by 1851
Abstract
In view of a general formula for higher order derivatives of the ratio of two differentiable functions, the authors establish the first form for the Maclaurin power series expansion of a logarithmic expression in term of determinants of special Hessenberg matrices whose elements [...] Read more.
In view of a general formula for higher order derivatives of the ratio of two differentiable functions, the authors establish the first form for the Maclaurin power series expansion of a logarithmic expression in term of determinants of special Hessenberg matrices whose elements involve the Bernoulli numbers. On the other hand, for comparison, the authors recite and revise the second form for the Maclaurin power series expansion of the logarithmic expression in terms of the Bessel zeta functions and the Bernoulli numbers. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nonlinear Analysis, Optimization and Related Topics)
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