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 751
Special Issue Editor
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
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 calculus
- fractional calculus
- optimal transport
- stochastic systems
- machine learning applications
- multiscale modeling
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