Emerging Applications and Theoretical Advances in Variational Methods, Functional Analysis, and Mathematical Optimization

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 744

Special Issue Editor


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Guest Editor
1. CIMA—Centro de Investigação em Matemática e Aplicações, Department of Mathematics, ISEL-Higher Institute of Engineering of Lisbon, Lisbon, Portugal
2. CIMOSM, Centro de Investigação em Modelação e Optimização de Sistemas Multifuncionais, ISEL-Higher Institute of Engineering of Lisbon, Lisbon, Portugal
Interests: mathematical modelling; numerical methods; eigenvalue; PDEs; isogeometric analysis; finite element analysis; structural vibration

Special Issue Information

Dear Colleagues,

This special issue aims to explore the latest developments in variational calculus, highlighting both theoretical advances and innovative applications. Variational calculus, which has long played a central role in mathematics and physics, is now experiencing a resurgence of interest due to its applications in emerging fields such as machine learning, quantum mechanics, and complex systems. This issue will serve as a platform for researchers to showcase cutting-edge work that bridges traditional methods with contemporary challenges.

We invite submissions addressing, but not limited to, the following areas:

  • Nonlocal and Fractional Variational Calculus: Extending classical principles to nonlocal interactions and fractional calculus models, with applications in physics and engineering.
  • Geometric and Optimal Transport Theories: Modern geometric methods, including links between variational calculus and optimal transport, applied to problems in economics, image processing, and physics.
  • Stochastic and Quantum Variational Principles: Incorporating randomness and quantum effects in variational frameworks for the study of stochastic systems and quantum mechanics.
  • Machine Learning and Data-Driven Methods: Leveraging variational principles to solve optimization problems in machine learning, artificial intelligence, and big data.
  • Multiscale and Complex Systems: Applications in multiscale modeling, complex systems, and materials science where variational methods offer powerful tools for analysis and optimization.
  • Classical Methods Revisited: New insights into classical problems, revisiting established variational approaches in light of recent theoretical developments.

Dr. José Alberto Rodrigues
Guest Editor

Manuscript Submission Information

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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 calculus
  • fractional calculus
  • optimal transport
  • stochastic systems
  • machine learning applications
  • multiscale modeling

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Published Papers (1 paper)

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Research

19 pages, 1037 KiB  
Article
Convergence Analysis for System of Cayley Generalized Variational Inclusion on q-Uniformly Banach Space
by Mohd Falahat Khan, Syed Shakaib Irfan and Iqbal Ahmad
Axioms 2025, 14(5), 361; https://doi.org/10.3390/axioms14050361 - 12 May 2025
Viewed by 214
Abstract
This paper is devoted to the analysis of a system of generalized variational inclusion problems involving α-averaged and Cayley operators within the framework of a q-uniformly smooth Banach space. We demonstrate that the problem can be reformulated as an equivalent fixed-point [...] Read more.
This paper is devoted to the analysis of a system of generalized variational inclusion problems involving α-averaged and Cayley operators within the framework of a q-uniformly smooth Banach space. We demonstrate that the problem can be reformulated as an equivalent fixed-point equation and propose an iterative method based on the fixed-point approach to obtain the solution. Furthermore, we establish the existence of solutions and analyze the convergence properties of the proposed algorithm under suitable conditions. To validate the effectiveness of the proposed iterative method, we provide a numerical result supported by a computational graph and a convergence plot, illustrating its performance and efficiency. Full article
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