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Axioms
Special Issues
Advances and Applications in Mathematical Modeling and Optimization
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Advances and Applications in Mathematical Modeling and Optimization

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

Deadline for manuscript submissions: 30 August 2026 | Viewed by 710

Special Issue Editor

Prof. Dr. Glenn Ledder

E-Mail Website
Guest Editor
Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE 68588, USA
Interests: mathematical modeling; epidemiology; dynamical systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue focuses very broadly on mathematical optimization. Papers may primarily be focused on developments in mathematical methods, developments in numerical methods, applications of optimization in mathematical models, or any combination of these areas. Papers on mathematical or numerical methods should be careful to explain how the new method fits into the overall context of optimization methods and should show how the new method improves on the body of optimization methods. Papers on applications of optimization should be careful to describe the context for the optimization model and justify all modeling and mathematical assumptions. 

All areas of optimization will be considered: continuous, discrete, and mixed optimization of control vectors and the calculus of variations and optimal control.

Prof. Dr. Glenn Ledder
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 250 words) can be sent to the Editorial Office for assessment.

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
  • numerical optimization
  • continuous optimization
  • discrete optimization
  • mixed optimization
  • nonlinear optimization
  • calculus of variations
  • optimal control

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

Published Papers (2 papers)

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Research

25 pages, 848 KB  
Article
A Fuzzy Stochastic DEA Model Considering an Input–Output Structure
by Lei Deng and Chong Li
Axioms 2026, 15(5), 376; https://doi.org/10.3390/axioms15050376 - 17 May 2026
Viewed by 163
Abstract
Traditional DEA models can neither effectively handle fuzzy random variables nor achieve a complete ranking of decision-making units (DMUs). Based on the conventional fuzzy stochastic DEA model, this study introduces an exponential distribution extension. By incorporating fuzzy random variables, it significantly simplifies the [...] Read more.
Traditional DEA models can neither effectively handle fuzzy random variables nor achieve a complete ranking of decision-making units (DMUs). Based on the conventional fuzzy stochastic DEA model, this study introduces an exponential distribution extension. By incorporating fuzzy random variables, it significantly simplifies the deterministic transformation of chance-constrained models. Moreover, most existing DEA ranking methods only consider the relative efficiencies among DMUs while ignoring their internal structural characteristics. To address this issue, we develop a deterministic model for the exponentially extended fuzzy stochastic DEA and design a weight formula that reflects the internal input–output structure of each DMU. This approach makes the complete ranking of DMUs more reasonable and better aligned with practical situations. Finally, the rationality and effectiveness of the proposed model are verified through a comparative analysis of rankings obtained from different DEA models. The results indicate that the input–output structure within a decision-making unit plays a significant role in its efficiency ranking. Full article
(This article belongs to the Special Issue Advances and Applications in Mathematical Modeling and Optimization)
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17 pages, 473 KB  
Article
A Subspace Derivative-Free Conjugate Gradient Method for Solving Nonlinear Monotone Equations with Convex Constraints
by Zongxu Li, Zhuo Fang, Mingyuan Cao, Yueting Yang, Ruobing Mei and Siqi Liu
Axioms 2026, 15(5), 351; https://doi.org/10.3390/axioms15050351 - 9 May 2026
Viewed by 208
Abstract
We propose a novel subspace derivative-free conjugate gradient method for solving large-scale nonlinear monotone equations with convex constraints. At each iteration, the search direction is constructed by minimizing a quadratic model within a subspace spanned by the current negative function value vector and [...] Read more.
We propose a novel subspace derivative-free conjugate gradient method for solving large-scale nonlinear monotone equations with convex constraints. At each iteration, the search direction is constructed by minimizing a quadratic model within a subspace spanned by the current negative function value vector and the two most recent search directions. The algorithm incorporates a hyperplane projection technique to generate feasible iterative points. Under reasonable assumptions, we establish the global convergence and R-linear convergence rate of the proposed method. Extensive numerical experiments on benchmark problems demonstrate that the new algorithm significantly outperforms state-of-the-art derivative-free methods in terms of number of iterations, function evaluations, and CPU time. The results confirm the efficiency and robustness of the proposed approach for solving large-scale monotone systems. Full article
(This article belongs to the Special Issue Advances and Applications in Mathematical Modeling and Optimization)
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