Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Bothina El-Sobky, Yousria Abo-Elnaga, Abd Allah A. Mousa and Mohamed A. El-Shorbagy
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Bothina El-Sobky: Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Qism Bab Sharqi 21568, Egypt
Yousria Abo-Elnaga: Department of Basic Science, Higher Technological Institute, Tenth of Ramadan City 44629, Egypt
Abd Allah A. Mousa: Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Mohamed A. El-Shorbagy: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Mathematics, 2021, vol. 9, issue 13, 1-20

Abstract: In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

Keywords: nonlinear programming problem; penalty method; barrier method; trust-region mechanism; global convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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