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Symmetry
Special Issues
Advanced Optimization Methods and Their Applications
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Advanced Optimization Methods and Their Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 October 2024 | Viewed by 2812

Special Issue Editors

Dr. Jianchao Bai

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Guest Editor
Associate Professor, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China
Interests: fundamental algorithms for big data and Artificial Intelligence; numerical algebra and optimization
Prof. Dr. Qiyu Jin

E-Mail Website
Guest Editor
School of Mathematical Science, Inner Mongolia University, Hohhot, China
Interests: biomedical image processing; big data analysis; deep learning; machine learning
Prof. Dr. Yuchao Tang

E-Mail Website
Guest Editor
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Interests: optimization model; algorithm and its application in image processing

Special Issue Information

Dear Colleagues,

With the development of big data and artificial intelligence, the development of efficient and straightforward optimization methods and the establishment of their convergence theory have become crucial. Furthermore, optimization plays a critical role in numerous other fields such as image processing, stochastic learning, signal processing, and computer vision. This Special Issue aims to disseminate some high-level manuscripts to the community on recent advanced optimization methods and their applications, which involves symmetric matrices or tensors related to the topics of Symmetry. It seeks to strengthen and deepen the understanding of the mathematical methodology of image processing and analysis by encouraging the quantitative comparison and performance evaluation. 

This Special issue of Symmetry is open to all fields of computational optimization and imaging science, from theoretical research to practical applications, with a particular emphasis on some advanced optimization algorithms and image processing, machine learning, and computer vision. Topics of interest include, but are not limited to:

  1. Development of novel models for various image processing and analysis problems;
  2. Optimization methods in machine learning;
  3. Stochastic first-order methods;
  4. Inexact optimization methods;
  5. Operator splitting methods and their theoretical analysis;
  6. Modern optimization methods for linear and nonlinear inverse problems.

Dr. Jianchao Bai
Prof. Dr. Qiyu Jin
Prof. Dr. Yuchao Tang
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. Symmetry 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

  • development of novel models for various image processing and analysis problems
  • optimization methods in machine learning
  • stochastic first-order methods
  • inexact optimization methods
  • operator splitting methods and their theoretical analysis
  • modern optimization methods for linear and nonlinear inverse problems

Published Papers (4 papers)

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Research

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20 pages, 1381 KiB  
Article
A Relaxed Inertial Method for Solving Monotone Inclusion Problems with Applications
by Chunxiang Zong, Yuchao Tang and Guofeng Zhang
Symmetry 2024, 16(4), 466; https://doi.org/10.3390/sym16040466 - 11 Apr 2024
Viewed by 373
Abstract
We study a relaxed inertial forward–backward–half-forward splitting approach with variable step size to solve a monotone inclusion problem involving a maximal monotone operator, a cocoercive operator, and a monotone Lipschitz operator. The convergence of the sequence of iterations generated by the discretisations of [...] Read more.
We study a relaxed inertial forward–backward–half-forward splitting approach with variable step size to solve a monotone inclusion problem involving a maximal monotone operator, a cocoercive operator, and a monotone Lipschitz operator. The convergence of the sequence of iterations generated by the discretisations of a continuous-time dynamical system is established under suitable conditions. Given the challenges associated with computing the resolvent of the composite operator, the proposed method is employed to tackle the composite monotone inclusion problem. Additionally, a convergence analysis is conducted under certain conditions. To demonstrate the effectiveness of the algorithm, numerical experiments are performed on the image deblurring problem. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Their Applications)
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19 pages, 2263 KiB  
Article
Semi-Proximal ADMM for Primal and Dual Robust Low-Rank Matrix Restoration from Corrupted Observations
by Weiwei Ding, Youlin Shang, Zhengfen Jin and Yibao Fan
Symmetry 2024, 16(3), 303; https://doi.org/10.3390/sym16030303 - 05 Mar 2024
Viewed by 745
Abstract
The matrix nuclear norm minimization problem has been extensively researched in recent years due to its widespread applications in control design, signal and image restoration, machine learning, big data problems, and more. One popular model is nuclear norm minimization with the l2 [...] Read more.
The matrix nuclear norm minimization problem has been extensively researched in recent years due to its widespread applications in control design, signal and image restoration, machine learning, big data problems, and more. One popular model is nuclear norm minimization with the l2-norm fidelity term, but it is only effective for those problems with Gaussian noise. A nuclear norm minimization problem with the l1-norm fidelity term has been studied in this paper, which can deal with the problems with not only non-Gaussian noise but also Gaussian noise or their mixture. Moreover, it also keeps the efficiency for the noiseless case. Given the nonsmooth proposed model, we transform it into a separated form by introducing an auxiliary variable and solve it by the semi-proximal alternating direction method of multipliers (sPADMM). Furthermore, we first attempt to solve its dual problem by sPADMM. Then, the convergence guarantees for the aforementioned algorithms are given. Finally, some numerical studies are dedicated to show the robustness of the proposed model and the effectiveness of the presented algorithms. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Their Applications)
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20 pages, 767 KiB  
Article
A Gradient-Based Algorithm with Nonmonotone Line Search for Nonnegative Matrix Factorization
by Wenbo Li and Xiaolu Shi
Symmetry 2024, 16(2), 154; https://doi.org/10.3390/sym16020154 - 29 Jan 2024
Viewed by 660
Abstract
In this paper, we first develop an active set identification technique, and then we suggest a modified nonmonotone line search rule, in which a new parameter formula is introduced to control the degree of the nonmonotonicity of line search. By using the modified [...] Read more.
In this paper, we first develop an active set identification technique, and then we suggest a modified nonmonotone line search rule, in which a new parameter formula is introduced to control the degree of the nonmonotonicity of line search. By using the modified line search and the active set identification technique, we propose a global convergent method to solve the NMF based on the alternating nonnegative least squares framework. In addition, the larger step size technique is exploited to accelerate convergence. Finally, a large number of numerical experiments are carried out on synthetic and image datasets, and the results show that our presented method is effective in calculating speed and solution quality. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Their Applications)
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Other

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0 pages, 238 KiB  
Brief Report
On Solving the Set Orienteering Problem
by Roberto Montemanni and Derek H. Smith
Symmetry 2024, 16(3), 340; https://doi.org/10.3390/sym16030340 - 12 Mar 2024
Viewed by 586
Abstract
In the Set Orienteering Problem, a single vehicle, leaving from and returning to a depot, has to serve some customers, each one associated with a given spacial location. Customers are grouped in clusters and a given prize is collected once a customer in [...] Read more.
In the Set Orienteering Problem, a single vehicle, leaving from and returning to a depot, has to serve some customers, each one associated with a given spacial location. Customers are grouped in clusters and a given prize is collected once a customer in a cluster is visited. The prize associated with a cluster can be collected at most once. Travel times among locations are provided, together with a maximum available mission time, which normally makes it impossible to visit all the clusters. The target is to design a route for the vehicle that maximizes the total prize collected within the given time limit. In this study, building on the recent literature, we present new preprocessing rules and a new constraint programming model for the problem. Thanks to the symmetry exploitation carried out by the constraint programming solver, new state-of-the-art results are established. Full article
(This article belongs to the Special Issue Advanced Optimization Methods and Their Applications)
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