Font Size: a A A

Research And Application Of Superiorization Algorithm For Convex Optimization Problems

Posted on:2021-02-17Degree:MasterType:Thesis
Country:ChinaCandidate:W CuiFull Text:PDF
GTID:2370330611468675Subject:Mathematics
Abstract/Summary:PDF Full Text Request
Proximal gradient algorithm is an effective method for solving the zero point of convex optimization problem.On this basis,based on the Superiorization algorithm framework proposed by Censor in recent years,we discuss the perturbed proximal gradient algorithm to solve a class of non-smooth combination convex optimization problems.On the one hand,the general and promotion on the perturbed proximal gradient algorithm from two aspects: one is the practical application of the algorithm itself,do promotion,so that the stronger the applicability of the algorithm,a wider range of applications;the two is to pay attention to the proximal gradient algorithm in infinite dimensional space is generally not strong convergence in nature,the perturbed proximal gradient algorithm and compression operator convex combination(called viscosity proximal gradient algorithm),obtain a strong convergence results.On the other hand,the application of Superiorization algorithm in proximal gradient algorithm is also studied in this paper.Because the Superiorization algorithm depends on the original algorithm of bounded perturbation resilience properties,one of the main work of this paper is through the two algorithms mentioned above proved that the proximal gradient algorithm and viscosity proximal gradient algorithm bounded perturbation resilience properties,and on this basis,gives the corresponding algorithms of Superiorization format.In addition,the paper also points out that the bounded perturbation of the original algorithm is used as the internal disturbance,and its form can actually be transformed into the external disturbance form of the proposed algorithm,thus providing proof of original algorithm with bounded perturbations in a direction of thinking recovery properties.Finally this paper gives the application and numerical algorithm in linear inverse problem of the operator cases.
Keywords/Search Tags:proximal gradient algorithm, bounded perturbation resilience, Superiorization, compression operator, linear inverse problems
PDF Full Text Request
Related items