A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems

This study is devoted to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for constrained optimization problems. First, the active-set strategy was used with a penalty and Newton's interior poin...

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Main Authors: Bothina El-Sobky, Yousria Abo-Elnaga, Gehan Ashry
Format: Article
Language:English
Published: AIMS Press 2025-02-01
Series:AIMS Mathematics
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Online Access:https://www.aimspress.com/article/doi/10.3934/math.2025117
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author Bothina El-Sobky
Yousria Abo-Elnaga
Gehan Ashry
author_facet Bothina El-Sobky
Yousria Abo-Elnaga
Gehan Ashry
author_sort Bothina El-Sobky
collection DOAJ
description This study is devoted to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for constrained optimization problems. First, the active-set strategy was used with a penalty and Newton's interior point method to convert a nonlinearly constrained optimization problem to an equivalent nonlinear unconstrained optimization problem. Second, a nonmonotone trust region was utilized to guarantee convergence from any starting point to the stationary point. Third, a global convergence theory for the proposed algorithm was presented under some assumptions. Finally, the proposed algorithm was tested by well-known test problems (the CUTE collection); three engineering design problems were resolved, and the results were compared with those of other respected optimizers. Based on the results, the suggested approach generally provides better approximation solutions and requires fewer iterations than the other algorithms under consideration. The performance of the proposed algorithm was also investigated, and computational results clarified that the suggested algorithm was competitive and better than other optimization algorithms.
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issn 2473-6988
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series AIMS Mathematics
spelling doaj-art-8316748fd4ea4cc0aa2bf2cd855fb5b62025-08-20T02:26:19ZengAIMS PressAIMS Mathematics2473-69882025-02-011022509254010.3934/math.2025117A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problemsBothina El-Sobky0Yousria Abo-Elnaga1Gehan Ashry2Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, EgyptDepartment of basic science, Tenth of Ramadan City, Higher Technological Institute, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, EgyptThis study is devoted to incorporating a nonmonotone strategy with an automatically adjusted trust-region radius to propose a more efficient hybrid of trust-region approaches for constrained optimization problems. First, the active-set strategy was used with a penalty and Newton's interior point method to convert a nonlinearly constrained optimization problem to an equivalent nonlinear unconstrained optimization problem. Second, a nonmonotone trust region was utilized to guarantee convergence from any starting point to the stationary point. Third, a global convergence theory for the proposed algorithm was presented under some assumptions. Finally, the proposed algorithm was tested by well-known test problems (the CUTE collection); three engineering design problems were resolved, and the results were compared with those of other respected optimizers. Based on the results, the suggested approach generally provides better approximation solutions and requires fewer iterations than the other algorithms under consideration. The performance of the proposed algorithm was also investigated, and computational results clarified that the suggested algorithm was competitive and better than other optimization algorithms.https://www.aimspress.com/article/doi/10.3934/math.2025117active setpenalty methodinterior pointnonmonotone trust regionglobal convergence
spellingShingle Bothina El-Sobky
Yousria Abo-Elnaga
Gehan Ashry
A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems
AIMS Mathematics
active set
penalty method
interior point
nonmonotone trust region
global convergence
title A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems
title_full A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems
title_fullStr A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems
title_full_unstemmed A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems
title_short A nonmonotone trust region technique with active-set and interior-point methods to solve nonlinearly constrained optimization problems
title_sort nonmonotone trust region technique with active set and interior point methods to solve nonlinearly constrained optimization problems
topic active set
penalty method
interior point
nonmonotone trust region
global convergence
url https://www.aimspress.com/article/doi/10.3934/math.2025117
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