On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point...

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Detalles Bibliográficos
Autores principales: Prusińska, Agnieszka, Szkatuła, Krzysztof, Tret’yakov, Alexey
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8071127/
https://www.ncbi.nlm.nih.gov/pubmed/33920784
http://dx.doi.org/10.3390/e23040465
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author Prusińska, Agnieszka
Szkatuła, Krzysztof
Tret’yakov, Alexey
author_facet Prusińska, Agnieszka
Szkatuła, Krzysztof
Tret’yakov, Alexey
author_sort Prusińska, Agnieszka
collection PubMed
description This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.
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spelling pubmed-80711272021-04-26 On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems Prusińska, Agnieszka Szkatuła, Krzysztof Tret’yakov, Alexey Entropy (Basel) Article This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities. MDPI 2021-04-15 /pmc/articles/PMC8071127/ /pubmed/33920784 http://dx.doi.org/10.3390/e23040465 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Prusińska, Agnieszka
Szkatuła, Krzysztof
Tret’yakov, Alexey
On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems
title On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems
title_full On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems
title_fullStr On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems
title_full_unstemmed On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems
title_short On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems
title_sort on the locally polynomial complexity of the projection-gradient method for solving piecewise quadratic optimisation problems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8071127/
https://www.ncbi.nlm.nih.gov/pubmed/33920784
http://dx.doi.org/10.3390/e23040465
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