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Axioms
Special Issues
New Developments in Analysis of Variational Inequalities and Related Fields
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New Developments in Analysis of Variational Inequalities and Related Fields

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 2348

Special Issue Editor

Dr. Savin Treanţă

E-Mail Website
Guest Editor
Department of Applied Mathematics, Faculty of Applied Sciences, University Politehnica of Bucharest, 060042 Bucharest, Romania
Interests: variational and functional analysis; optimization methods; control theory; differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The present Special Issue, entitled “New Developments in Analysis of Variational Inequalities and Related Fields”, will cover modeling, mathematical analysis, optimal control, integral inequality problems, variational inequalities with applications, and their numerical treatment. More specifically, this Special Issue aims to develop essential tools for solving problems that arise in various branches of mathematical analysis, such as variational problems, nonlinear optimization problems, equilibrium problems, complementarity problems, integral and differential equations. We hope this initiative proves to be attractive to researchers specializing in the above-mentioned fields. Original research and review articles are welcome. Contributions may be submitted continuously before the deadline, and, after a peer-review process, are to be selected for publication based on their quality and relevance.

Dr. Savin Treanţă
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 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

  • variational inequalities
  • integral inequalities
  • variational models
  • optimal control
  • generalized convexity
  • generalized differentiability
  • optimization problems

Published Papers (3 papers)

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Research

13 pages, 249 KiB  
Article
A Self Adaptive Three-Step Numerical Scheme for Variational Inequalities
by Kubra Sanaullah, Saleem Ullah and Najla M. Aloraini
Axioms 2024, 13(1), 57; https://doi.org/10.3390/axioms13010057 - 18 Jan 2024
Viewed by 760
Abstract
In this paper, we introduce a new three-step iterative scheme for finding the common solutions of the variational inequality using the technique of updating the solution. We suggest, iterative algorithms involving three-steps for the predictor-corrector method of variational inequality in real Hilbert spaces [...] Read more.
In this paper, we introduce a new three-step iterative scheme for finding the common solutions of the variational inequality using the technique of updating the solution. We suggest, iterative algorithms involving three-steps for the predictor-corrector method of variational inequality in real Hilbert spaces H. Our results include the Takahashi and Toyoda, extra gradient, Mann and Noor iterations as special cases. We also investigate the convergence criteria of the three-step iterative scheme. As special cases, the earlier findings are included in our results, which can be seen as an advancement and improvement over the previous investigation. This is a new refinement in our existing literature and previously known algorithms. A numerical example is given to illustrate the efficiency and performance of the proposed self-adaptive scheme. Full article
(This article belongs to the Special Issue New Developments in Analysis of Variational Inequalities and Related Fields)
14 pages, 285 KiB  
Article
On Sufficiency Conditions for Some Robust Variational Control Problems
by Tareq Saeed and Savin Treanţă
Axioms 2023, 12(7), 705; https://doi.org/10.3390/axioms12070705 - 20 Jul 2023
Viewed by 589
Abstract
We study the sufficient optimality conditions for a class of fractional variational control problems involving data uncertainty in the cost functional. Concretely, by using the parametric technique, we prove the sufficiency of the robust necessary optimality conditions by considering convexity, quasi-convexity, strictly quasi-convexity, [...] Read more.
We study the sufficient optimality conditions for a class of fractional variational control problems involving data uncertainty in the cost functional. Concretely, by using the parametric technique, we prove the sufficiency of the robust necessary optimality conditions by considering convexity, quasi-convexity, strictly quasi-convexity, and/or monotonic quasi-convexity assumptions of the involved functionals. Full article
(This article belongs to the Special Issue New Developments in Analysis of Variational Inequalities and Related Fields)
13 pages, 302 KiB  
Article
Robust Optimality Conditions for a Class of Fractional Optimization Problems
by Tareq Saeed
Axioms 2023, 12(7), 673; https://doi.org/10.3390/axioms12070673 - 07 Jul 2023
Cited by 1 | Viewed by 644
Abstract
In this paper, by considering the parametric technique, we study a class of fractional optimization problems involving data uncertainty in the objective functional. We formulate and prove the robust Karush-Kuhn-Tucker necessary optimality conditions and provide their sufficiency by considering the convexity and/or concavity [...] Read more.
In this paper, by considering the parametric technique, we study a class of fractional optimization problems involving data uncertainty in the objective functional. We formulate and prove the robust Karush-Kuhn-Tucker necessary optimality conditions and provide their sufficiency by considering the convexity and/or concavity assumptions of the involved functionals. In addition, to complete the study, an illustrative example is presented. Full article
(This article belongs to the Special Issue New Developments in Analysis of Variational Inequalities and Related Fields)
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