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Recent Advances in Nonsmooth Optimization and Analysis

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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 August 2023) | Viewed by 5372

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Special Issue Editor

Dr. Sorin-Mihai Grad

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Guest Editor

Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria
Interests: convex analysis; convex optimization; monotone operators; vector optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonsmooth optimization problems cover various real-world applications. In this Special Issue of “Recent Advances in Nonsmooth Optimization Analysis”, we are open for contributions presenting the theory and numerical methods that can be modeled for solving nonsmooth optimization and real-life problems.

We welcome innovative submissions from all areas of Nonsmooth Optimization, including Convex and Generalized Convex Optimization, with an emphasis on algorithms for solving such problems, with or without practical applications.

Dr. Sorin-Mihai Grad
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 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. 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 1600 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
convex optimization
nonsmooth analysis
convex analysis

Published Papers (4 papers)

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Research

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27 pages, 510 KiB

Open AccessArticle

Lipschitz Continuity Results for a Class of Parametric Variational Inequalities and Applications to Network Games

by Mauro Passacantando and Fabio Raciti

Algorithms 2023, 16(10), 458; https://doi.org/10.3390/a16100458 - 26 Sep 2023

Viewed by 980

Abstract

We consider a class of finite-dimensional variational inequalities where both the operator and the constraint set can depend on a parameter. Under suitable assumptions, we provide new estimates for the Lipschitz constant of the solution, which considerably improve previous ones. We then consider the problem of computing the mean value of the solution with respect to the parameter and, to this end, adapt an algorithm devised to approximate a Lipschitz function whose analytic expression is unknown, but can be evaluated in arbitrarily chosen sample points. Finally, we apply our results to a class of Nash equilibrium problems, and generalized Nash equilibrium problems on networks. Full article

(This article belongs to the Special Issue Recent Advances in Nonsmooth Optimization and Analysis)

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16 pages, 449 KiB

Open AccessArticle

Optimal Maintenance Schedule for a Wind Power Turbine with Aging Components

by Quanjiang Yu, Ola Carlson and Serik Sagitov

Algorithms 2023, 16(7), 334; https://doi.org/10.3390/a16070334 - 13 Jul 2023

Cited by 2 | Viewed by 1401

Abstract

Wind power is one of the most important sources of renewable energy available today. A large part of the cost of wind energy is due to the cost of maintaining wind power equipment. When a wind turbine component fails to function, it might need to be replaced under circumstances that are less than ideal. This is known as corrective maintenance. To minimize unnecessary costs, a more active maintenance policy based on the life expectancy of the key components is preferred. Optimal scheduling of preventive maintenance activities requires advanced mathematical modeling. In this paper, an optimal preventive maintenance algorithm is designed using the renewal-reward theorem. In the multi-component setting, our approach involves a new idea of virtual maintenance that allows us to treat each replacement event as a renewal event even if some components are not replaced by new ones. The proposed optimization algorithm is applied to a four-component model of a wind turbine, and the optimal maintenance plans are computed for various initial conditions. The modeling results clearly show the benefit of PM planning compared to a pure CM strategy (about 30% lower maintenance cost). Full article

(This article belongs to the Special Issue Recent Advances in Nonsmooth Optimization and Analysis)

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14 pages, 406 KiB

Open AccessArticle

On the Adaptive Penalty Parameter Selection in ADMM

by Serena Crisci, Valentina De Simone and Marco Viola

Algorithms 2023, 16(6), 264; https://doi.org/10.3390/a16060264 - 25 May 2023

Viewed by 1236

Abstract

Many data analysis problems can be modeled as a constrained optimization problem characterized by nonsmooth functionals, often because of the presence of

ℓ_{1}

-regularization terms. One of the most effective ways to solve such problems is through the Alternate Direction Method of [...] Read more.

Many data analysis problems can be modeled as a constrained optimization problem characterized by nonsmooth functionals, often because of the presence of

ℓ_{1}

-regularization terms. One of the most effective ways to solve such problems is through the Alternate Direction Method of Multipliers (ADMM), which has been proved to have good theoretical convergence properties even if the arising subproblems are solved inexactly. Nevertheless, experience shows that the choice of the parameter

τ

penalizing the constraint violation in the Augmented Lagrangian underlying ADMM affects the method’s performance. To this end, strategies for the adaptive selection of such parameter have been analyzed in the literature and are still of great interest. In this paper, starting from an adaptive spectral strategy recently proposed in the literature, we investigate the use of different strategies based on Barzilai–Borwein-like stepsize rules. We test the effectiveness of the proposed strategies in the solution of real-life consensus logistic regression and portfolio optimization problems. Full article

(This article belongs to the Special Issue Recent Advances in Nonsmooth Optimization and Analysis)

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Review

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30 pages, 1491 KiB

Open AccessReview

A State of the Art Review of Systems of Linear Inequalities and Related Observability Problems

by Enrique Castillo

Algorithms 2023, 16(8), 356; https://doi.org/10.3390/a16080356 - 25 Jul 2023

Viewed by 1071

Abstract

This work is a short review of the state of the art aiming to contribute to the use, disclosure, and propagation of systems of linear inequalities in real life, teaching, and research. It shows that the algebraic structure of their solutions consists of the sum of a linear subspace, an acute cone, and a polytope, and that adequate software exists to obtain, in their simplest forms, these three components. The work describes, based on orthogonality and polarity, homogeneous and complete systems of inequalities, the associated compatibility problems, and their relations with convex polyhedra and polytopes, which are the only possible solution for bounded problems, the most common in real practice. The compatibility and the observability problems, including their symbolic forms, are analyzed and solved, identifying the subsets of unknowns with unique solutions and those unbounded, important items of information with practical relevance in artificial intelligence and automatic learning. Having infinitely many solutions of a given problem allows us to find solutions when some of the assumptions fail and unexpected constraints come into play, a common situation for engineers. The linear programming problem becomes trivial when the set of all solutions is available and all solutions are obtained, contrary to the case of standard programs that provide only one solution. Several examples of applications to several areas of knowledge are presented, illustrating the advantages of solving these systems of inequalities. Full article

(This article belongs to the Special Issue Recent Advances in Nonsmooth Optimization and Analysis)

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