Properties of the Quadratic Transformation of Dual Variables : научное издание

Krutikov Vladimir; Tovbis Elena; Bykov Anatoly; Stanimirovic Predrag; Chernova Ekaterina; Kazakovtsev Lev

Дополнительные ссылки: eLibrary

База данных: Каталог библиотеки СФУ

Библиографическое описание: Properties of the Quadratic Transformation of Dual Variables : научное издание / V. V. Krutikov [et al.]. - Текст : непосредственный // Algorithms. - 2023. - Т. 16, № 3. - P. 148. - This work was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-15-2022-1121). - ISSN 1999-4893, DOI 10.3390/a16030148.

Аннотация: We investigate a solution of a convex programming problem with a strongly convex objective function based on the dual approach. A dual optimization problem has constraints on the positivity of variables. We study the methods and properties of transformations of dual variables that enable us to obtain an unconstrained optimization problem. We investigate the previously known method of transforming the components of dual variables in the form of their modulus (modulus method). We show that in the case of using the modulus method, the degree of the degeneracy of the function increases as it approaches the optimal point. Taking into account the ambiguity of the gradient in the boundary regions of the sign change of the new dual function variables and the increase in the degree of the function degeneracy, we need to use relaxation subgradient methods (RSM) that are difficult to implement and that can solve non-smooth non-convex optimization problems with a high degree of elongation of level surfaces. We propose to use the transformation of the components of dual variables in the form of their square (quadratic method). We prove that the transformed dual function has a Lipschitz gradient with a quadratic method of transformation. This enables us to use efficient gradient methods to find the extremum. The above properties are confirmed by a computational experiment. With a quadratic transformation compared to a modulus transformation, it is possible to obtain a solution of the problem by relaxation subgradient methods and smooth function minimization methods (conjugate gradient method and quasi-Newtonian method) with higher accuracy and lower computational costs. The noted transformations of dual variables were used in the program module for calculating the maximum permissible emissions of enterprises (MPE) of the software package for environmental monitoring of atmospheric air (ERA-AIR).

Год издания: 2023

Авторы: Krutikov Vladimir , Tovbis Elena , Bykov Anatoly , Stanimirovic Predrag , Chernova Ekaterina , Kazakovtsev Lev

Источник: Algorithms

Выпуск: Т. 16, № 3

Номера страниц: 148

Держатель оригинала документа: Federal Research Center for Information and Computational Technologies, Kemerovo State University, Reshetnev Siberian State University of Science and Technology, Siberian Federal University, University of Nis

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