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Optimization Theory, Method and Application, 2nd Edition
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Optimization Theory, Method and Application, 2nd Edition

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

Deadline for manuscript submissions: 20 January 2026 | Viewed by 215

Special Issue Editors

Prof. Dr. Chao Zhang

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Guest Editor
School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
Interests: non-smooth optimization; stochastic programming; data mining
Special Issues, Collections and Topics in MDPI journals
Dr. Yang Zhou

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Guest Editor
School of Mathematics and Statistics, Shandong Normal University, Jinan 250061, China
Interests: optimization theory and method
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Optimization theory, methods, and applications play increasingly important roles in modern society, assisting in solving optimization challenges arising from nonsmooth optimization problems, stochastic programming, and integer programming, to name a few. This Special Issue will focus on collecting recent research works on topics such as optimality conditions and duality theory, and algorithms and applications for difficult optimization problems, including nonsmooth optimization, stochastic programming, variational inequalities, bilevel programming, integer programming, and combinatorial optimization. Topics of interest include, but are not limited to, the following:

  • Optimality conditions for various optimization problems;
  • Duality theory for various optimization problems;
  • Smoothing algorithms for nonsmooth optimization;
  • Stochastic approximation algorithms;
  • Proximal algorithms for nonsmooth optimization;
  • Cutting plane algorithms;
  • Heuristics and metaheuristics for combinatorial optimization;
  • Applications in economics;
  • Applications in transportation;
  • Applications in data mining;
  • Applications in network design and machine learning.

Prof. Dr. Chao Zhang
Dr. Yang Zhou
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. 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

  • optimality theory
  • dual theory
  • nonsmooth optimization
  • smoothing method
  • stochastic approximation method
  • integer programming
  • combinatorial optimization
  • metaheuristics and heuristics
  • applications

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Published Papers (1 paper)

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Research

31 pages, 363 KiB  
Article
Dynamic Stepsize Techniques in DR-Submodular Maximization
by Yanfei Li, Min Li, Qian Liu and Yang Zhou
Mathematics 2025, 13(9), 1447; https://doi.org/10.3390/math13091447 - 28 Apr 2025
Viewed by 142
Abstract
The Diminishing-Return (DR)-submodular function maximization problem has garnered significant attention across various domains in recent years. Classic methods often employ continuous greedy or Frank–Wolfe approaches to tackle this problem; however, high iteration and subproblem solver complexity are typically required to control the approximation [...] Read more.
The Diminishing-Return (DR)-submodular function maximization problem has garnered significant attention across various domains in recent years. Classic methods often employ continuous greedy or Frank–Wolfe approaches to tackle this problem; however, high iteration and subproblem solver complexity are typically required to control the approximation ratio effectively. In this paper, we introduce a strategy that employs a binary search to find the dynamic stepsize, integrating it into traditional algorithm frameworks to address problems with different constraint types. We demonstrate that algorithms using this dynamic stepsize strategy can achieve comparable approximation ratios to those using a fixed stepsize strategy. In the monotone case, the iteration complexity is O∥∇F(0)∥1ϵ−1, while in the non-monotone scenario, it is On+∥∇F(0)∥1ϵ−1, where F denotes the objective function. We then apply this strategy to solving stochastic DR-submodular function maximization problems, obtaining corresponding iteration complexity results in a high-probability form. Furthermore, theoretical examples as well as numerical experiments validate that this stepsize selection strategy outperforms the fixed stepsize strategy. Full article
(This article belongs to the Special Issue Optimization Theory, Method and Application, 2nd Edition)
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