A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems

In algorithm development, symmetry plays a vital part in managing optimization problems in scientific models. The aim of this work is to propose a new accelerated method for finding a common point of convex minimization problems and then use the fixed point of the forward-backward operator to explain and analyze a weak convergence result of the proposed algorithm in real Hilbert spaces under certain conditions. As applications, we demonstrate the suggested method for solving image inpainting and image restoration problems.

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“…By (15) and condition (A2), we have that (14) and Lemma 3, we obtain that lim k→∞ z k − z * exists. By ( 9) and ( 10), we obtain…”

Section: Resultsmentioning

confidence: 84%

“…For the past decade, many algorithms based on fixed point method were proposed to solve the problem (1), see [4,8,[11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

An Algorithm for Solving Common Points of Convex Minimization Problems with Applications

2022

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A New Accelerated Algorithm for Convex Bilevel Optimization Problems and Applications in Data Classification

et al. 2022

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In the development of algorithms for convex optimization problems, symmetry plays a very important role in the approximation of solutions in various real-world problems. In this paper, based on a fixed point algorithm with the inertial technique, we proposed and study a new accelerated algorithm for solving a convex bilevel optimization problem for which the inner level is the sum of smooth and nonsmooth convex functions and the outer level is a minimization of a smooth and strongly convex function over the set of solutions of the inner level. Then, we prove its strong convergence theorem under some conditions. As an application, we apply our proposed algorithm as a machine learning algorithm for solving some data classification problems. We also present some numerical experiments showing that our proposed algorithm has a better performance than the five other algorithms in the literature, namely BiG-SAM, iBiG-SAM, aiBiG-SAM, miBiG-SAM and amiBiG-SAM.

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A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems

Cited by 2 publications

References 35 publications

An Algorithm for Solving Common Points of Convex Minimization Problems with Applications

An Algorithm for Solving Common Points of Convex Minimization Problems with Applications

A New Accelerated Algorithm for Convex Bilevel Optimization Problems and Applications in Data Classification

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