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Axioms
Special Issues
Advances in Nonlinear and Convex Analysis
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Advances in Nonlinear and Convex Analysis

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 10576

Special Issue Editors

Prof. Dr. Yeong-Cheng Liou

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Guest Editor
1. Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, Kaohsiung 82444, Taiwan
2. Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 82444, Taiwan
Interests: fixed point problem; optimization problem; nonlinear analysis; machine (deep) learning; iterative method; operations research
Prof. Dr. Ching-Feng Wen

E-Mail Website
Guest Editor
Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
Interests: fixed point theory; theory and algorithms on variational inequalities; set-valued and variational analysis; nonlinear analysis; optimization; well-posedness and optimal control
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jen-Chih Yao

E-Mail Website
Guest Editor
1. Research Center for Interneural Computing, China Medical University Hospital, Taichung City 404332, Taiwan
2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
Interests: vector optimization; fixed point theory; variational inequalities; complementarity problems; variational analysis; equilibrium problems; optimal control; generalized convexity and generalized monotonicity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear and convex analysis is a rapidly growing area of mathematics, with numerous applications in optimization, control theory, machine (deep) learning, economics, engineering, management and other disciplines. In recent years, with the tool of nonlinear analysis, various reformulations for optimization problems and techniques in analyzing the convergence of algorithms have found new directions. This issue is devoted to the publication of original articles of current interest in every theoretical, computational and applicational aspect of nonlinear analysis, variational analysis, convex analysis, multivalued analysis, non-smooth analysis, fixed point theory and optimization theory, as well as their applications to science, engineering, economics, management, healthcare and other disciplines.

The purpose of this Special Issue is to pay tribute to the significant contributions and recent advances in theories, methods, and applications, including, but not limited to, the following fields:

  • Nonlinear, convex, multivalued, variational and nonsmooth analysis;
  • Fixed point, coincidence point and best proximity point theory;
  • Optimization and optimal control theory;
  • Algorithms and numerical analysis for nonlinear problems;
  • Nonlinear and variational methods for ODEs and PDEs;
  • Inverse, ill-posed and perturbed problems;
  • Game theory and dynamical systems;
  • Data mining, machine and deep learning;
  • Applications in engineering, economic, management, medicine and healthcare.

Prof. Dr. Yeong-Cheng Liou
Prof. Dr. Ching-Feng Wen
Prof. Dr. Jen-Chih Yao
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. Axioms 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

  • nonlinear analysis
  • convex analysis
  • multivalued analysis
  • variational analysis
  • nonsmooth analysis
  • optimization
  • optimal control
  • fixed point problem
  • variational inequality
  • equilibrium problem
  • iterative method
  • machine (deep) learning
  • data mining

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 papers)

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Research

11 pages, 281 KiB  
Article
On Robust Global Error Bounds for a Class of Uncertain Piecewise Linear Inequality Systems
by Wen Tan, Xiaole Guo and Xiangkai Sun
Axioms 2022, 11(10), 497; https://doi.org/10.3390/axioms11100497 - 23 Sep 2022
Viewed by 1231
Abstract
This paper is concerned with the radius of robust global error bounds for an uncertain piecewise linear inequality system where the uncertain data are assumed to be in polytope uncertain sets. We first present a dual characterization for robust global error bounds of [...] Read more.
This paper is concerned with the radius of robust global error bounds for an uncertain piecewise linear inequality system where the uncertain data are assumed to be in polytope uncertain sets. We first present a dual characterization for robust global error bounds of this uncertain piecewise linear inequality system. Then, we establish upper and lower bounds for the radius of robust global error bounds of the system of uncertain piecewise linear inequalities in terms of the Minkowski function generalized by the polytope uncertain sets. Moreover, we also investigate robust global error bounds for this uncertain piecewise linear inequality system when the uncertain polytope sets are symmetric sets. Full article
(This article belongs to the Special Issue Advances in Nonlinear and Convex Analysis)
20 pages, 432 KiB  
Article
Proximal Linearized Iteratively Reweighted Algorithms for Nonconvex and Nonsmooth Optimization Problem
by Juyeb Yeo and Myeongmin Kang
Axioms 2022, 11(5), 201; https://doi.org/10.3390/axioms11050201 - 24 Apr 2022
Cited by 1 | Viewed by 2390
Abstract
The nonconvex and nonsmooth optimization problem has been attracting increasing attention in recent years in image processing and machine learning research. The algorithm-based reweighted step has been widely used in many applications. In this paper, we propose a new, extended version of the [...] Read more.
The nonconvex and nonsmooth optimization problem has been attracting increasing attention in recent years in image processing and machine learning research. The algorithm-based reweighted step has been widely used in many applications. In this paper, we propose a new, extended version of the iterative convex majorization–minimization method (ICMM) for solving a nonconvex and nonsmooth minimization problem, which involves famous iterative reweighted methods. To prove the convergence of the proposed algorithm, we adopt the general unified framework based on the Kurdyka–Łojasiewicz inequality. Numerical experiments validate the effectiveness of the proposed algorithm compared to the existing methods. Full article
(This article belongs to the Special Issue Advances in Nonlinear and Convex Analysis)
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15 pages, 338 KiB  
Article
Accelerated Modified Tseng’s Extragradient Method for Solving Variational Inequality Problems in Hilbert Spaces
by Godwin Amechi Okeke, Mujahid Abbas, Manuel De la Sen and Hira Iqbal
Axioms 2021, 10(4), 248; https://doi.org/10.3390/axioms10040248 - 1 Oct 2021
Cited by 3 | Viewed by 2204
Abstract
The aim of this paper is to propose a new iterative algorithm to approximate the solution for a variational inequality problem in real Hilbert spaces. A strong convergence result for the above problem is established under certain mild conditions. Our proposed method requires [...] Read more.
The aim of this paper is to propose a new iterative algorithm to approximate the solution for a variational inequality problem in real Hilbert spaces. A strong convergence result for the above problem is established under certain mild conditions. Our proposed method requires the computation of only one projection onto the feasible set in each iteration. Some numerical examples are presented to support that our proposed method performs better than some known comparable methods for solving variational inequality problems. Full article
(This article belongs to the Special Issue Advances in Nonlinear and Convex Analysis)
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15 pages, 312 KiB  
Article
A Tseng-Type Algorithm with Self-Adaptive Techniques for Solving the Split Problem of Fixed Points and Pseudomonotone Variational Inequalities in Hilbert Spaces
by Li-Jun Zhu and Yeong-Cheng Liou
Axioms 2021, 10(3), 152; https://doi.org/10.3390/axioms10030152 - 10 Jul 2021
Cited by 3 | Viewed by 1775
Abstract
In this paper, we survey the split problem of fixed points of two pseudocontractive operators and variational inequalities of two pseudomonotone operators in Hilbert spaces. We present a Tseng-type iterative algorithm for solving the split problem by using self-adaptive techniques. Under certain assumptions, [...] Read more.
In this paper, we survey the split problem of fixed points of two pseudocontractive operators and variational inequalities of two pseudomonotone operators in Hilbert spaces. We present a Tseng-type iterative algorithm for solving the split problem by using self-adaptive techniques. Under certain assumptions, we show that the proposed algorithm converges weakly to a solution of the split problem. An application is included. Full article
(This article belongs to the Special Issue Advances in Nonlinear and Convex Analysis)
13 pages, 287 KiB  
Article
Variational-Like Inequality Problem Involving Generalized Cayley Operator
by Zahoor Ahmad Rather, Rais Ahmad and Ching-Feng Wen
Axioms 2021, 10(3), 133; https://doi.org/10.3390/axioms10030133 - 26 Jun 2021
Cited by 3 | Viewed by 1784
Abstract
This article deals with the study of a variational-like inequality problem which involves the generalized Cayley operator. We compare our problem with a fixed point equation, and based on it we construct an iterative algorithm to obtain the solution of our problem. Convergence [...] Read more.
This article deals with the study of a variational-like inequality problem which involves the generalized Cayley operator. We compare our problem with a fixed point equation, and based on it we construct an iterative algorithm to obtain the solution of our problem. Convergence analysis as well as stability analysis are studied. Full article
(This article belongs to the Special Issue Advances in Nonlinear and Convex Analysis)
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