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: 31 December 2024 | Viewed by 2636

Special Issue Editor

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

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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 826
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
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
Cited by 2 | Viewed by 672
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
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 - 7 Jul 2023
Cited by 2 | Viewed by 718
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
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