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Algorithms
Special Issues
Numerical Optimization and Algorithms: 4th Edition
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Numerical Optimization and Algorithms: 4th Edition

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Algorithms for Multidisciplinary Applications".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 743

Special Issue Editors

Prof. Dr. Dunhui Xiao

E-Mail Website
Guest Editor
School of Mathematical Sciences, Tongji University, Shanghai 200092, China
Interests: AI; machine learning; model reduction; finite element analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shuai (Steven) Li

E-Mail Website
Guest Editor
Faculty of Information Technology and Electrical Engineering, University of Oulu, 90570 Oulu, Finland
Interests: robotics and automation; intelligent control and optimization; signal processing; embedded systems; robotic manipulation; autonomous manufacturing; multi-robot coordination
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Numerical algorithms and optimization are widely used in fields of science and engineering, such as physics, environment, mechanics, biology, data science, economics, finance, and so on. These problems are complex, highly nonlinear, and difficult to predict. Over the last decade, computational problems have become popular and have gained much attention due to the improved computer performance, computing methods, and the rapid development of data science technology. However, these developments have also raised various issues and challenges, such as high non-linearity, the curse of dimensionality, uncertainty, complexity, and so on. Therefore, these challenges urgently need to be addressed by developing new numerical algorithms, such as graph theory, optimization algorithms, algebra, uncertainty, data science or analysis, new differential equations solving algorithms and methods, probability, and statistics algorithms and methods.

This Special Issue deals with various numerical algorithms in the fields of both science and engineering.

Prof. Dr. Dunhui Xiao
Prof. Dr. Shuai Li
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. Algorithms 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 1800 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

  • graph theory
  • optimization
  • algebra
  • uncertainty
  • data science
  • differential equations
  • probability and statistics
  • numerical algorithms

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Related Special Issue

Published Papers (1 paper)

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Research

41 pages, 762 KB  
Article
MCMC Methods: From Theory to Distributed Hamiltonian Monte Carlo over PySpark
by Christos Karras, Leonidas Theodorakopoulos, Aristeidis Karras, George A. Krimpas, Charalampos-Panagiotis Bakalis and Alexandra Theodoropoulou
Algorithms 2025, 18(10), 661; https://doi.org/10.3390/a18100661 - 17 Oct 2025
Viewed by 527
Abstract
The Hamiltonian Monte Carlo (HMC) method is effective for Bayesian inference but suffers from synchronization overhead in distributed settings. We propose two variants: a distributed HMC (DHMC) baseline with synchronized, globally exact gradient evaluations and a communication-avoiding leapfrog HMC (CALF-HMC) method that interleaves [...] Read more.
The Hamiltonian Monte Carlo (HMC) method is effective for Bayesian inference but suffers from synchronization overhead in distributed settings. We propose two variants: a distributed HMC (DHMC) baseline with synchronized, globally exact gradient evaluations and a communication-avoiding leapfrog HMC (CALF-HMC) method that interleaves local surrogate micro-steps with a single–global Metropolis–Hastings correction per trajectory. Implemented on Apache Spark/PySpark and evaluated on a large synthetic logistic regression (N=107, d=100, workers J∈{4,8,16,32}), DHMC attained an average acceptance of 0.986, mean ESS of 1200, and wall-clock of 64.1 s per evaluation run, yielding ≈18.7 ESS/s; CALF-HMC achieved an acceptance of 0.942, mean ESS of 5.1, and 14.8 s, i.e., ≈0.34 ESS/s under the tested surrogate configuration. While DHMC delivered higher ESS/s due to robust mixing under conservative integration, CALF-HMC reduced the per-trajectory runtime and exhibited more favorable scaling as inter-worker latency increased. The study contributes (i) a systems-oriented communication cost model for distributed HMC, (ii) an exact, communication-avoiding leapfrog variant, and (iii) practical guidance for ESS/s-optimized tuning on clusters. Full article
(This article belongs to the Special Issue Numerical Optimization and Algorithms: 4th Edition)
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