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Algorithms
Special Issues
Nonsmooth Optimization and Its Applications
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Nonsmooth Optimization and Its Applications

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

Deadline for manuscript submissions: closed (31 December 2025) | Viewed by 3928

Special Issue Editor

Dr. Nargiz Sultanova

E-Mail Website
Guest Editor
Institute of Innovation, Science and Sustainability, Federation University Australia, Ballarat, VIC 3350, Australia
Interests: nonsmooth optimization and its various applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We would like to invite submissions of manuscripts dedicated to recent advancements in the field of nonsmooth optimization and its applications.

Nonsmooth optimization refers to a class of optimization problems where the objective function and/or constraints are not differentiable. It provides powerful tools with which to solve problems that traditional smooth methods cannot tackle effectively. In real-life applications, nonsmoothness often emerges from the inherent nature of systems or models that exhibit abrupt changes, discontinuities, or piecewise behavior. These problems arise in a variety of fields, such as machine learning, image and signal processing, economics and finance, control systems, and others. In some cases, nonsmooth terms are intentionally introduced into models for computational efficiency in order to approximate the otherwise complex smooth behavior of systems.

This Special Issue aims to bring together the latest research on the theoretical principles, algorithmic developments, and practical applications of nonsmooth optimization.

Dr. Nargiz Sultanova
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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

  • nonsmooth optimization
  • non-differentiable optimization
  • subgradient methods
  • signal processing
  • image processing
  • bundle methods
  • machine learning
  • applications of nonsmooth optimization

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Published Papers (5 papers)

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Research

14 pages, 306 KB  
Article
Properties of Some Classes of Structured Minmaxmin Problems
by Narges Araboljadidi, Manlio Gaudioso, Giovanni Giallombardo and Giovanna Miglionico
Algorithms 2026, 19(2), 140; https://doi.org/10.3390/a19020140 - 9 Feb 2026
Viewed by 213
Abstract
Minmaxmin problems are well suited for representing some significant decision making problems, where both strategic and tactical decisions are to be made, at different points of time, in the presence of uncertain scenarios. We survey some basic properties and introduce some classes of [...] Read more.
Minmaxmin problems are well suited for representing some significant decision making problems, where both strategic and tactical decisions are to be made, at different points of time, in the presence of uncertain scenarios. We survey some basic properties and introduce some classes of structured minmaxmin problems. The main focus is on linear and bilinear minmaxmin problems, which reduce to classic nonsmooth optimization problems. Moreover, two classes of examples are introduced to highlight the practical role of such formulations. The first one is related to the optimal capacity planning of a production–distribution system, and the second one deals with product pricing and distribution in a profit-maximization framework. Finally, focusing on the capacity-planning and product-distribution problem, a computational study has been carried out to illustrate the practical performance of a cutting-plane and proximity-control algorithm for solving the resulting convex nonsmooth minmaxmin model. The numerical results confirm the robustness of the approach and its scalability with respect to both the network size and the number of scenarios. Full article
(This article belongs to the Special Issue Nonsmooth Optimization and Its Applications)
15 pages, 595 KB  
Article
Collision of an Obstacle by an Elastic Bar in a Gravity Field: Solution with Discontinuous Velocity and Space-Time Primal-Dual Active Set Algorithm
by Victor A. Kovtunenko
Algorithms 2026, 19(1), 88; https://doi.org/10.3390/a19010088 - 20 Jan 2026
Viewed by 152
Abstract
A class of one-dimensional dynamic impact models is investigated with respect to non-smooth velocities using variational inequalities and space-time finite element approximation. For the problem of collision of a rigid obstacle by an elastic bar in the gravitational field, a benchmark based on [...] Read more.
A class of one-dimensional dynamic impact models is investigated with respect to non-smooth velocities using variational inequalities and space-time finite element approximation. For the problem of collision of a rigid obstacle by an elastic bar in the gravitational field, a benchmark based on particular solutions to the wave equation is constructed on a partition of rectangle domains. The full discretization of the collision problem is carried out over a uniform space-time triangulation and extended to distorted meshes. For the solution of the corresponding variational inequality, a semi-smooth Newton-based primal-dual active set algorithm is applied. Numerical experiments demonstrate advantages over time-step approximation: a high-precision numerical solution is computed in a few iterations without any spurious oscillations. Full article
(This article belongs to the Special Issue Nonsmooth Optimization and Its Applications)
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13 pages, 285 KB  
Article
A Duality Framework for Mathematical Programs with Tangential Subdifferentials
by Vandana Singh, Shashi Kant Mishra and Abdelouahed Hamdi
Algorithms 2026, 19(1), 45; https://doi.org/10.3390/a19010045 - 5 Jan 2026
Viewed by 330
Abstract
The aim of this article is to study duality results for nonsmooth mathematical programs with equilibrium constraints in terms of tangential subdifferentials. We study the Wolfe-type dual problem under the convexity assumptions and a Mond–Weir-type dual problem is also formulated under convexity and [...] Read more.
The aim of this article is to study duality results for nonsmooth mathematical programs with equilibrium constraints in terms of tangential subdifferentials. We study the Wolfe-type dual problem under the convexity assumptions and a Mond–Weir-type dual problem is also formulated under convexity and generalized convexity assumptions for MPEC by using tangential subdifferentials. We establish weak duality and the two dual programs by assuming tangentially convex functions and also obtain strong duality theorems by assuming generalized standard Abadie constraint qualification. Full article
(This article belongs to the Special Issue Nonsmooth Optimization and Its Applications)
14 pages, 549 KB  
Article
Poroelastic Medium with Non-Penetrating Crack Driven by Hydraulic Fracture: FEM Approximation Using HHT-α and Semi-Smooth Newton Methods
by Victor A. Kovtunenko and Olena M. Atlasiuk
Algorithms 2025, 18(9), 579; https://doi.org/10.3390/a18090579 - 13 Sep 2025
Cited by 2 | Viewed by 1040
Abstract
A new class of poroelastic dynamic contact problems stemming from hydraulic fracture theory is introduced and studied. The two-phase medium consists of a solid phase and pores which are saturated with a Newtonian fluid. The porous body contains a fluid-driven crack endowed with [...] Read more.
A new class of poroelastic dynamic contact problems stemming from hydraulic fracture theory is introduced and studied. The two-phase medium consists of a solid phase and pores which are saturated with a Newtonian fluid. The porous body contains a fluid-driven crack endowed with non-penetration conditions for the opposite crack surfaces. The poroelastic model is described by a coupled system of hyperbolic–parabolic partial differential equations under the unilateral constraint imposed on displacement. After full discretization using finite-element and Hilber–Hughes–Taylor methods, the well-posedness of the resulting variational inequality is established. Formulation of the complementarity conditions with the help of a minimum-based merit function is used for the semi-smooth Newton method of solution presented in the form of a primal–dual active set algorithm which is tested numerically. Full article
(This article belongs to the Special Issue Nonsmooth Optimization and Its Applications)
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16 pages, 649 KB  
Article
Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions
by David Levin and Nira Gruberger
Algorithms 2025, 18(6), 335; https://doi.org/10.3390/a18060335 - 3 Jun 2025
Cited by 1 | Viewed by 1063
Abstract
We address the challenge of efficiently approximating piecewise smooth functions, particularly those with jump discontinuities. Given function values on a uniform grid over a domain Ω in Rd, we present a novel B-spline-based approximation framework, using new adaptable quasi-interpolation operators. This [...] Read more.
We address the challenge of efficiently approximating piecewise smooth functions, particularly those with jump discontinuities. Given function values on a uniform grid over a domain Ω in Rd, we present a novel B-spline-based approximation framework, using new adaptable quasi-interpolation operators. This approach integrates discontinuity detection techniques, allowing the quasi-interpolation operator to selectively use points from only one side of a discontinuity in both one- and two-dimensional cases. Among a range of candidate operators, the most suitable quasi-interpolation scheme is chosen to ensure high approximation accuracy and efficiency, while effectively suppressing spurious oscillations in the vicinity of discontinuities. Full article
(This article belongs to the Special Issue Nonsmooth Optimization and Its Applications)
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