Monoton kapsama problemini çözmek için alternatif eylemsiz ileri-geri-ileri ayırma algoritması ve uygulamaları

Abstract

Maksimum monoton bir operatör ile tek değerli, aynı zamanda Lipschitz sürekli olan monoton bir operatörün toplamının sıfırlarını bulmak amacıyla tasarlanmış alternatif eylemsiz ileri-geri-ileri algoritmasını sunuyoruz. Bu çalışma, Tseng'in ileri-geri-ileri algoritmasını alternatif atalet etkilerini ekleyerek genişletmeyi amaçlamaktadır. Ardından, geliştirilmiş algoritmamızı konveks minimizasyon problemlerini ele almak için uyguluyoruz. Ana konular arasında monoton kapsama problemi, ileri-geri-ileri algoritması, alternatif eylemsiz yöntemi ve konveks minimizasyon problemleri yer almaktadır. Son olarak, önerdiğimiz yaklaşımın görüntü iyileştirme uygulamasını inceleyerek etkinliğini ve uygulanabilirliğini vurguluyoruz.

Keywords

• Monoton Kapsama Problemi
• İleri-geri-ileri algoritması
• Alternatif Atalet Metot
• Konveks minimizasyon problemi
• görüntü iyileştirme problemi

An alternating inertial forward-backward-forward algorithm for solving monotone inclusion problem and its applications

Abstract

We present an alternating inertial forward-backward-forward algorithm designed to find the zeros of the sum of a maximally monotone operator and a single-valued monotone operator that is also Lipschitz continuous. This study aims to extend Tseng’s forward-backward-forward algorithm by incorporating alternating inertial effects. We then apply our enhanced algorithm to address convex minimization problems. Key topics include the monotone inclusion problem, forward-backward-forward algorithm, the alternating inertial method, and convex minimization problems. Lastly, we explore the application of our proposed approach in image restoration, emphasizing its effectiveness and adaptability.

Keywords

• Monotone inclusion problem
• forward-backward-forward algorithm
• alternating inertial method
• convex minimization problem
• image restoration problem.

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