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Journals / European Journal of Pure and Applied Mathematics (elektronik) / 2010 / Cilt: 3 - Sayı: 1

On the cross-entropic regularization method for solving min-max problems

Jianyu Lİ
Lili ZHANG
Xingsi Lİ
Pages
98–106
Publication Date
2022-11-05
DOI
—
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AI Summary & Key Takeaways

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

At last, the condition number is analyzed, and the results reveal that the smoothing method of multipliers is stable for any fixed smoothing parameter.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A smoothing method of multipliers which is a natural result of cross-entropic regularization for min-max problems is analyzed.
📊
Key Findings & Data:As a smoothing technique, we first show how the smooth approximation yields the first order information on the behavior of max function.
💡
Conclusion & Impact:At last, the condition number is analyzed, and the results reveal that the smoothing method of multipliers is stable for any fixed smoothing parameter.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

A smoothing method of multipliers which is a natural result of cross-entropic regularization for min-max problems is analyzed. As a smoothing technique, we first show how the smooth approximation yields the first order information on the behavior of max function. Then under suitable assumptions, some basic properties including the Hessian are given. At last, the condition number is analyzed, and the results reveal that the smoothing method of multipliers is stable for any fixed smoothing parameter.

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Cite This Article

Lİ, J., ZHANG, L., Lİ, X. (2022). On the cross-entropic regularization method for solving min-max problems. European Journal of Pure and Applied Mathematics (elektronik), Cilt: 3 - Sayı: 1, 98–106. https://ajindex.com/articles/650429

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