Mathematical Programming and Optimization Algorithms

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D2: Operations Research and Fuzzy Decision Making".

Deadline for manuscript submissions: 31 January 2026 | Viewed by 805

Special Issue Editors


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Guest Editor
Departamento de Ingeniería Industrial, Universidad de Santiago de Chile (USACH), Santiago 9170124, Chile
Interests: integer programming; linear programming; mathematical programming

E-Mail Website
Guest Editor
Departamento de Ingeniería Industrial, Universidad de Santiago de Chile (USACH), Santiago 9170124, Chile
Interests: supply chain modeling and optimization; multi-criteria decision making; agent-based simulation

Special Issue Information

Dear Colleagues

In this Special Issue Mathematical Programming and Optimization Algorithms, we welcome articles related to mathematical programming; integer programming; linear programming and network flow; nonlinear programming, theory, and algorithms; algorithm complexity; the applications of operations research; and discrete and stochastic optimization. Topics also include branch-and-bound, branch-and-cut, and cutting plane algorithms; multi-objective optimization, deterministic and non-deterministic algorithms; stochastic programming; approximation algorithms; and multi-criteria methods. Advances in and results for classical mathematical programming problems such as the knapsack, lot sizing, traveling salesman, set cover, assignment, and uncapacitated facility location problems, among other similar problems, are also covered in this Special Issue.

This Special Issue accepts high-quality papers containing original research results and review articles of exceptional merit.

Dr. Ivan Derpich
Dr. Juan M. Sepúlveda
Guest Editors

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Keywords

  • applied mathematics
  • mathematical optimization
  • integer programming
  • branch and bound
  • applications of operations research
  • multi-criteria methods
  • stochastic programming
  • approximation algorithms

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Published Papers (1 paper)

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Research

15 pages, 428 KiB  
Article
A Forward–Backward–Forward Algorithm for Quasi-Variational Inequalities in the Moving Set Case
by Nevena Mijajlović, Ajlan Zajmović and Milojica Jaćimović
Mathematics 2025, 13(12), 1956; https://doi.org/10.3390/math13121956 - 13 Jun 2025
Viewed by 240
Abstract
This paper addresses the challenge of solving quasi-variational inequalities (QVIs) by developing and analyzing a forward–backward–forward algorithm from a continuous and iterative perspective. QVIs extend classical variational inequalities by allowing the constraint set to depend on the decision variable, a formulation that is [...] Read more.
This paper addresses the challenge of solving quasi-variational inequalities (QVIs) by developing and analyzing a forward–backward–forward algorithm from a continuous and iterative perspective. QVIs extend classical variational inequalities by allowing the constraint set to depend on the decision variable, a formulation that is particularly useful in modeling various problems. A critical computational challenge in these settings is the expensive nature of projection operations, especially when closed-form solutions are unavailable. To mitigate this, we consider the moving set case and propose a forward–backward–forward algorithm that requires only one projection per iteration. Under the assumption that the operator is strongly monotone, we establish that the continuous trajectories generated by the corresponding dynamical system converge exponentially to the unique solution of the QVI. We extend Tseng’s well-known forward–backward–forward algorithm for variational inequalities by adapting it to the more complex framework of QVIs. We prove that it converges when applied to strongly monotone QVIs and derive its convergence rate. We perform numerical implementations of our proposed algorithm and give numerical comparisons with other related gradient projection algorithms for quasi-variational inequalities in the literature. Full article
(This article belongs to the Special Issue Mathematical Programming and Optimization Algorithms)
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