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

Year 2025, Volume: 27 Issue: 2, 654 - 666, 15.07.2025

Ebru Altıparmak

https://doi.org/10.25092/baunfbed.1549042

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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