Mathematical Optimization, Variational Inequalities and Equilibrium Problems: Theory and Applications
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".
Deadline for manuscript submissions: 1 June 2026 | Viewed by 21
Special Issue Editors
Interests: equilibrium problems; generalized monotonicity; computational and numerical methods; mathematical biology
Interests: mathematical optimization; equilibrium problems; variational inequalities; generalized convexity
Special Issue Information
Dear colleagues,
This Special Issue aims to disseminate recent advances in mathematical optimizations, variational inequalities and equilibrium problems, emphasizing the links between them.
Variational inequalities theory was introduced as a tool for the study of partial differential equations principally drawn from mechanics, but since then it proved to be a powerful unifying instrument for the study of mathematical optimization and equilibrium problems, with results about the existence and uniqueness of solutions, duality, stability and sensitivity analysis, finding solving methods and providing algorithms together with convergence analysis for computational purposes. All these factors have resulted in it becoming a theoretical area in itself, leading to the study of generalizations in several directions, such as variational inclusions, set-valued variational inequalities and equilibrium problems or systems of these.
The concept of equilibrium is central in numerous disciplines, including economics, management science, operations research and engineering. The formulation and qualitative analysis of equilibrium problems and computation of equilibria appear in mathematical programming, complementarity theory, fixed-point theory, game theory and even optimal control theory. Equilibrium problems which can be formulated using variational inequalities include traffic network equilibrium problems, spatial price equilibrium problems, oligopolistic market equilibrium problems and financial equilibrium problems, as well as supply chain network equilibrium problems.
An optimization problem is characterized by its specific objective function, which needs to be maximized or minimized and, in some cases, satisfy a given set of constraints. Possible objective functions include expressions representing profits, costs, market shares, portfolio risks, etc. Possible constraints include limited budgets or resources, nonnegativity constraints on the variables, conservation equations, etc. Many constrained and unconstrained problems can be formulated in terms of variational inequalities or equilibrium problems.
This Special Issue will address the following non-exhaustive list of topics: discrete and continuous optimization, linear and nonlinear programming, operational research, classical and generalized equilibrium problems and variational inequalities, complementarity problems, game theory and fixed-point methods.
Authors are welcome to submit original and significant contributions on the above or other closely related areas, focusing on theoretical foundations, numerical and computational aspects, or real-life applications. Contributions may be submitted on a continuous basis before the deadline. After a peer-review process, submissions will be selected for publication based on their quality and relevance.
We look forward to receiving your valuable contributions.
Prof. Dr. Andrei-Dan Halanay
Dr. Miruna-Mihaela Beldiman
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
- mathematical optimization
- mathematical programming
- operational research
- equilibrium problems
- variational inequalities
- complementarity problems
- game theory
- fixed point methods
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