{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:27:42Z","timestamp":1760146062931,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T00:00:00Z","timestamp":1728345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the 2020 Shanghai Leading Talents Program of the Shanghai Municipal Human Resources and Social Security Bureau","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]},{"name":"the Innovation Program of Shanghai Municipal Education Commission","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]},{"name":"the Program for Outstanding Academic Leaders in Shanghai City","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Convex bilevel optimization problems (CBOPs) exhibit a vital impact on the decision-making process under the hierarchical setting when image restoration plays a key role in signal processing and computer vision. In this paper, a modified double inertial extragradient-like approach with a line search procedure is introduced to tackle the CBOP with constraints of the CFPP and VIP, where the CFPP and VIP represent a common fixed point problem and a variational inequality problem, respectively. The strong convergence analysis of the proposed algorithm is discussed under certain mild assumptions, where it constitutes both sections that possess a mutual symmetry structure to a certain extent. As an application, our proposed algorithm is exploited for treating the image restoration problem, i.e., the LASSO problem with the constraints of fractional programming and fixed-point problems. The illustrative instance highlights the specific advantages and potential infect of the our proposed algorithm over the existing algorithms in the literature, particularly in the domain of image restoration.<\/jats:p>","DOI":"10.3390\/sym16101324","type":"journal-article","created":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T12:03:49Z","timestamp":1728389029000},"page":"1324","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Modified Double Inertial Extragradient-like Approaches for Convex Bilevel Optimization Problems with VIP and CFPP Constraints"],"prefix":"10.3390","volume":"16","author":[{"given":"Yue","family":"Zeng","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3730-1475","authenticated-orcid":false,"given":"Lu-Chuan","family":"Ceng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liu-Fang","family":"Zheng","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xie","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,8]]},"reference":[{"key":"ref_1","first-page":"747","article-title":"The extragradient method for finding saddle points and other problems","volume":"12","author":"Korpelevich","year":"1976","journal-title":"Ekon. 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