A Novel Two-Step Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Image Recovery

被引：4

作者：

Wattanataweekul, Rattanakorn ^{[1
]}

Janngam, Kobkoon ^{[2
]}

Suantai, Suthep ^{[3
]}

机构：

[1] Ubon Ratchathani Univ, Fac Sci, Dept Math Stat & Comp, Ubon Ratchathani 34190, Thailand

[2] Chiang Mai Univ, Fac Sci, Dept Math, Grad Ph D Degree Program Math, Chiang Mai 50200, Thailand

[3] Chiang Mai Univ, Fac Sci, Res Ctr Optimizat & Computat Intelligence Big Data, Dept Math, Chiang Mai 50200, Thailand

来源：

MATHEMATICS | 2023年 / 11卷 / 16期

关键词：

convex bilevel optimization; forward-backward algorithms; image restoration problems; two-step inertial; viscosity approximation; FORWARD-BACKWARD ALGORITHM; APPROXIMATION METHODS; MONOTONE-OPERATORS; 1ST-ORDER METHOD; CONVERGENCE; REGRESSION; SHRINKAGE; ITERATION; SELECTION; MAPPINGS;

D O I：

10.3390/math11163518

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper introduces a novel two-step inertial algorithm for locating a common fixed point of a countable family of nonexpansive mappings. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve convex bilevel optimization problems. The method is further applied to the image recovery problem. Our numerical experiments show that the proposed method achieves faster convergence than other related methods in the literature.

引用

页数：20

共 44 条

[1] [Anonymous], 2009, Nonlinear analysis and convex analysis
[2] Strong convergence theorems for strongly nonexpansive sequences
Aoyama, Koji
Kimura, Yasunori
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (19) : 7537 - 7545
[3] Bauschke HH, 2011, CMS BOOKS MATH, P1, DOI 10.1007/978-1-4419-9467-7
[4] A first order method for finding minimal norm-like solutions of convex optimization problems
Beck, Amir
Sabach, Shoham
[J]. MATHEMATICAL PROGRAMMING, 2014, 147 (1-2) : 25 - 46
[5] A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, Amir
Teboulle, Marc
[J]. SIAM JOURNAL ON IMAGING SCIENCES, 2009, 2 (01): : 183 - 202
[6] WEAK CONVERGENCE OF AN ERGODIC ITERATION FOR SOLUTION OF VARIATIONAL INEQUALITIES FOR MONOTONE OPERATORS IN HILBERT-SPACE
BRUCK, RE
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1977, 61 (01) : 159 - 164
[7] Bussaban L, 2020, CARPATHIAN J MATH, V36, P35
[8] Proximal point algorithm controlled by a slowly vanishing term: Applications to hierarchical minimization
Cabot, A
[J]. SIAM JOURNAL ON OPTIMIZATION, 2005, 15 (02) : 555 - 572
[9] A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation
Chen, Dai-Qiang
Zhang, Hui
Cheng, Li-Zhi
[J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2012, 43 (03) : 167 - 179
[10] QUASI-NONEXPANSIVE ITERATIONS ON THE AFFINE HULL OF ORBITS: FROM MANN'S MEAN VALUE ALGORITHM TO INERTIAL METHODS
Combettes, Patrick L.
Glaudin, Lilian E.
[J]. SIAM JOURNAL ON OPTIMIZATION, 2017, 27 (04) : 2356 - 2380

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