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Journals / Fundamental Journal of Mathematics and Applications / 2023 / Cilt: 6 Sayı: 3

A New Smoothing Algorithm to Solve a System of Nonlinear Inequalities

Nurullah YILMAZ
Ayşegül KAYACAN
Pages
137–146
Publication Date
2023-09-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The new algorithm is applied to some numerical examples to show the efficiency of our algorithm.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the system of nonlinear inequalities (SNI) problem is investigated.
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Key Findings & Data:First, a SNI is reformulated as a system of nonsmooth and nonlinear equations (SNNE).
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Conclusion & Impact:The new algorithm is applied to some numerical examples to show the efficiency of our algorithm.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Iterative methods · Smoothing · System of non-linear inequalities.

Abstract

In this study, the system of nonlinear inequalities (SNI) problem is investigated. First, a SNI is reformulated as a system of nonsmooth and nonlinear equations (SNNE). Second, a new smoothing technique for the "$\max$" function is proposed and the smoothing technique is employed for each element of the SNNE. Then, a new smoothing algorithm is developed in order to solve SNNE by combining the smoothing technique with the iterative method. The new algorithm is applied to some numerical examples to show the efficiency of our algorithm.

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Cite This Article

YILMAZ, N., KAYACAN, A. (2023). A New Smoothing Algorithm to Solve a System of Nonlinear Inequalities. Fundamental Journal of Mathematics and Applications, Cilt: 6 Sayı: 3, 137–146. https://ajindex.com/articles/964186

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