Aims and scope

Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal.

Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.

Publication office: Taylor & Francis, Inc., 530 Walnut Street, Suite 850, Philadelphia, PA 19106.

Special Issue on Analysis and applications of data-driven methods
Submission Date: 2024-09-30

Special Issue Editor(s)

Andrea Aspri, University of Milan “La Statale”
andrea.aspri@unimi.it

Giovanni S. Alberti, University of Genoa
giovanni.alberti@unige.it

Otmar Scherzer, University of Vienna and RICAM
otmar.scherzer@univie.ac.at

In recent years, the interaction between data-driven and knowledge-driven methods is enjoying strong success within scientific communities, and especially in computational mathematics, in cases when the knowledge of the modelling is not fully available, or whenever the standard methods are computationally unfeasible. The use of machine learning has revolutionized several fields, including the numerical analysis of partial differential equations (PDEs), inverse problems, and compressed sensing. An essential contribution has been given by applied harmonic analysis, in the development of new ideas and methods in signal processing and approximation theory, providing an important tool to obtain a theoretical framework for machine learning theories.

The main goal of this Special Issue is to collect research contributes on various themes where analysis and machine learning play a crucial role, and where data- and physics-driven approaches are utilized, including PDEs, inverse problems, imaging, optimal control, and applied harmonic analysis. Possible topics are the theoretical and numerical analysis of data-driven regularization techniques, network architectures, neural operators for PDEs, deep generative models, and real-world applications of machine learning to the biomedical, engineering, and physical sciences.

Recommended topics include:

    Machine Learning for PDEs
    Data-driven regularization techniques
    Applied Harmonic Analysis
    Machine learning in infinite-dimensional spaces
    Analysis of Neural Networks
    Approximation theory
    Reinforcement learning
    Compressed sensing

Special Issue on Recent Developments in Inverse Problems – Dedicated to the 70th Birthday of Professor Bernd Hofmann
Submission Date: 2024-09-30

Special Issue Editor(s)

Akhtar A. Khan, Rochester Institute of Technology
aaksma@rit.edu

Robert Plato, University of Siegen
plato@mathematik.uni-siegen.de

Elena Resmerita, Alpen-Adria University of Klagenfurt
elena.resmerita@aau.at

Ronny Ramlau, Johannes Kepler University Linz and Radon Institute of Computational and Applied Mathematics
ronny.ramlau@jku.at

Frank Werner, University of Wuerzburg
frank.werner@uni-wuerzburg.de

Over the past few decades, Professor Bernd Hofmann has left an enduring impact across a spectrum of theoretical and computational facets of inverse problems. This special edition of the international journal "Numerical Functional Analysis and Optimization" is poised to recognize and celebrate Prof. Hofmann's profound contributions as a researcher of the highest caliber by gathering some of the most recent advancements in the dynamic and expanding field of inverse problems.