Logarithmic Penalty Function Approach for Solving Multi-Objective Geometric Programming Problems

Walid Hassan Jibrin¹ , Mansur Hassan² , Kabiru Suleiman³

1. Dept. of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria.
2. Dept. of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria.
3. Dept. of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria.

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.11 , pp.126-131, Nov-2024

Online published on Nov 30, 2024

Copyright © Walid Hassan Jibrin, Mansur Hassan, Kabiru Suleiman . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This paper presents a novel approach to solving Multi-Objective Geometric Programming Problems (MOGPP) using a Logarithmic Penalty Function (LPF) method. We introduce a transformation technique that converts the original multi-objective geometric programming problem into an equivalent single-objective problem. The proposed method is shown to satisfy Karush-Kuhn-Tucker (KKT) conditions, ensuring optimality of the solutions. Numerical examples are provided to demonstrate the effectiveness of the approach in comparison to existing methods. The proposed method shows improved convergence and solution quality across a range of test problems.

Key-Words / Index Term :
Multi-Objective, Optimization, Geometric Programming, Logarithmic Penalty Method, Pareto Optimality

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