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On convergence and complexity of the modified forward‐backward method involving new linesearches for convex minimization
Author(s) -
Kankam Kunrada,
Pholasa Nattawut,
Cholamjiak Prasit
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5420
Subject(s) - lipschitz continuity , convergence (economics) , mathematics , minification , convex optimization , range (aeronautics) , mathematical optimization , regular polygon , rate of convergence , constant (computer programming) , computational complexity theory , algorithm , computer science , mathematical analysis , geometry , economics , economic growth , channel (broadcasting) , computer network , materials science , composite material , programming language
In optimization theory, convex minimization problems have been intensively investigated in the current literature due to its wide range in applications. A major and effective tool for solving such problem is the forward‐backward splitting algorithm. However, to guarantee the convergence, it is usually assumed that the gradient of functions is Lipschitz continuous and the stepsize depends on the Lipschitz constant, which is not an easy task in practice. In this work, we propose the modified forward‐backward splitting method using new linesearches for choosing suitable stepsizes and discuss the convergence analysis including its complexity without any Lipschitz continuity assumption on the gradient. Finally, we provide numerical experiments in signal recovery to demonstrate the computational performance of our algorithm in comparison to some well‐known methods. Our reports show that the proposed algorithm has a good convergence behavior and can outperform the compared methods.