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Mathematics
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Numerical Optimization: Algorithms and Applications
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Numerical Optimization: Algorithms and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: closed (30 September 2025) | Viewed by 1685

Special Issue Editor

Dr. Xinguang Zhang

E-Mail Website
Guest Editor
1. School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China
2. Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia
Interests: nonlinear analysis on manifolds; optimization for process modeling; simulation and applications; fractional order differential equations; partial differential equation; critical points theory; nonlinear systems; fractional calculus; mathematical modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Optimization has a wide range of uses in science, engineering, economics, and industry. The practice of optimization depends not only on efficient and robust algorithms but also on good modeling techniques, careful interpretation of results and user-friendly software.

The development and improvement of optimization techniques are of great significance for the study of corresponding science problems. The aim of this Special Issue is to report on the latest achievements and recent development in the algorithms and applications for optimization problems, including in largescale optimization techniques such as interior-point methods, inexact Newton methods, limited-memory methods and some numerical optimizations that are not limited.

This Special Issue will collect high-quality original research articles as well as review articles in the above scope.

Dr. Xinguang Zhang
Guest Editor

Manuscript Submission Information

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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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • optimization for process modeling
  • numerical simulation of the optimization problems
  • optimization for process control
  • global optimization
  • stochastic optimization
  • robust optimization
  • multi-criteria optimization problems
  • operations research problems
  • optimization on graphs and networks
  • optimization in logistics
  • optimization of manufacturing processes
  • vehicle routing and other transportation problems
  • control-theoretic problems
  • exact solution algorithms
  • machine-learning
  • complexity issues

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Published Papers (2 papers)

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9 pages, 852 KB  
Article
A Fast Designed Thresholding Algorithm for Low-Rank Matrix Recovery with Application to Missing English Text Completion
by Haizhen He, Angang Cui and Hong Yang
Mathematics 2025, 13(19), 3135; https://doi.org/10.3390/math13193135 - 1 Oct 2025
Viewed by 250
Abstract
This article is proposing a fast version of adaptive iterative matrix designed thresholding (AIMDT) algorithm which is studied in our previous work. In AIMDT algorithm, a designed thresholding operator is studied to the problem of recovering the low-rank matrices. By adjusting the size [...] Read more.
This article is proposing a fast version of adaptive iterative matrix designed thresholding (AIMDT) algorithm which is studied in our previous work. In AIMDT algorithm, a designed thresholding operator is studied to the problem of recovering the low-rank matrices. By adjusting the size of the parameter, this designed operator can apply less bias to the singular values of a matrice. Using this proposed designed operator, the AIMDT algorithm has been generated to solve the matrix rank minimization problem, and the numerical experiments have shown the superiority of AIMDT algorithm. However, the AIMDT algorithm converges slowly in general. In order to recover the low-rank matrices more quickly, we present a fast AIMDT algorithm to recover the low-rank matrices in this paper. The numerical results on some random low-rank matrix completion problems and a missing English text completion problem show that the our proposed fast algorithm has much faster convergence than the previous AIMDT algorithm. Full article
(This article belongs to the Special Issue Numerical Optimization: Algorithms and Applications)
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50 pages, 6459 KB  
Article
A Novel Swarm Optimization Algorithm Based on Hive Construction by Tetragonula carbonaria Builder Bees
by Mildret Guadalupe Martínez Gámez and Hernán Peraza Vázquez
Mathematics 2025, 13(17), 2721; https://doi.org/10.3390/math13172721 - 24 Aug 2025
Viewed by 1034
Abstract
This paper introduces a new optimization problem-solving method based on how the stingless bee Tetragonula carbonaria builds and regulates temperature in the hive. The Tetragonula carbonaria Optimization Algorithm (TGCOA) models three different behaviors: strengthening the structure’s hive when it is cold, building combs [...] Read more.
This paper introduces a new optimization problem-solving method based on how the stingless bee Tetragonula carbonaria builds and regulates temperature in the hive. The Tetragonula carbonaria Optimization Algorithm (TGCOA) models three different behaviors: strengthening the structure’s hive when it is cold, building combs in a spiral pattern at medium temperatures, and stabilizing the hive when it is hot. These temperature-dependent strategies dynamically balance global exploitation and local exploration within the solution space, enabling a more efficient search. To validate the efficiency and effectiveness of the proposed method, the TGCOA algorithm was tested using ten unimodal and ten multimodal benchmark functions, twenty-eight constrained problems with dimensions set to 10, 30, 50, and 100 taken from the IEEE CEC 2017, and seven real-world engineering design challenges. Furthermore, it was compared with ten algorithms from the literature. Wilcoxon signed-rank and Friedman statistical tests were performed to assess the outcomes. The results on the benchmark problems showed that the approach outperformed 80% of the algorithms at a 5% significance level in the Wilcoxon signed-rank test and ranked first overall according to the Friedman test. Additionally, in multidimensional problems, the TGCOA was ranked first in dimensions 30, 50, and 100. Moreover, in engineering problems, the approach demonstrated a high capacity to solve constraint problems, obtaining better results than the algorithms that were compared. Full article
(This article belongs to the Special Issue Numerical Optimization: Algorithms and Applications)
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