TY  - JOUR
T1  - An alternating inertial forward-backward-forward algorithm for solving monotone inclusion problem and its applications
TT  - Monoton kapsama problemini çözmek için alternatif eylemsiz ileri-geri-ileri ayırma algoritması ve uygulamaları
AU  - Altıparmak, Ebru
PY  - 2025
DA  - July
Y2  - 2025
DO  - 10.25092/baunfbed.1549042
JF  - Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
JO  - BAUN Fen. Bil. Enst. Dergisi
PB  - Balıkesir Üniversitesi
WT  - DergiPark
SN  - 1301-7985
SP  - 654
EP  - 666
VL  - 27
IS  - 2
LA  - en
AB  - 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.
KW  - Monotone inclusion problem
KW  - forward-backward-forward algorithm
KW  - alternating inertial method
KW  - convex minimization problem
KW  - image restoration problem.
N2  - 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.
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UR  - https://doi.org/10.25092/baunfbed.1549042
L1  - https://dergipark.org.tr/tr/download/article-file/4209822
ER  -