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

Author

Listed:
  • 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
    Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt)

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.

Suggested Citation

  • Bothina El-Sobky & Yousria Abo-Elnaga & Abd Allah A. Mousa & Mohamed A. El-Shorbagy, 2021. "Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections," Mathematics, MDPI, vol. 9(13), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1551-:d:586977
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    References listed on IDEAS

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    1. Sakineh Tahmasebzadeh & Hamidreza Navidi & Alaeddin Malek, 2015. "Novel Interior Point Algorithms for Solving Nonlinear Convex Optimization Problems," Advances in Operations Research, Hindawi, vol. 2015, pages 1-7, September.
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    Cited by:

    1. Palanivel Kaliyaperumal & Amrit Das, 2022. "A Mathematical Model for Nonlinear Optimization Which Attempts Membership Functions to Address the Uncertainties," Mathematics, MDPI, vol. 10(10), pages 1-20, May.
    2. Luis Fernando Grisales-Noreña & Oscar Danilo Montoya & Brandon Cortés-Caicedo & Farhad Zishan & Javier Rosero-García, 2023. "Optimal Power Dispatch of PV Generators in AC Distribution Networks by Considering Solar, Environmental, and Power Demand Conditions from Colombia," Mathematics, MDPI, vol. 11(2), pages 1-20, January.

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