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

Bothina El-Sobky; Yousria Abo-Elnaga; Gehan Ashry; Bothina El-Sobky; Yousria Abo-Elnaga; Gehan Ashry

doi:10.3934/math.2025117

AIMS Mathematics

2025, Volume 10, Issue 2: 2509-2540. doi: 10.3934/math.2025117

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Research article

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

1.
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
2.
Department of basic science, Tenth of Ramadan City, Higher Technological Institute, Egypt

Received: 16 October 2024 Revised: 23 January 2025 Accepted: 29 January 2025 Published: 12 February 2025
MSC : 49M37, 65K05, 90C30, 90C55

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.
- active set,
- penalty method,
- interior point,
- nonmonotone trust region,
- global convergence
Citation: 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[J]. AIMS Mathematics, 2025, 10(2): 2509-2540. doi: 10.3934/math.2025117

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Abstract

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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