{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:37:37Z","timestamp":1760236657363,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,12]],"date-time":"2021-12-12T00:00:00Z","timestamp":1639267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Startup Fund of Xihua University","award":["RZ2000002862"],"award-info":[{"award-number":["RZ2000002862"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The underlying function in reproducing kernel Hilbert space (RKHS) may be degraded by outliers or deviations, resulting in a symmetry ill-posed problem. This paper proposes a nonconvex minimization model with \u21130-quasi norm based on RKHS to depict this degraded problem. The underlying function in RKHS can be represented by the linear combination of reproducing kernels and their coefficients. Thus, we turn to estimate the related coefficients in the nonconvex minimization problem. An efficient algorithm is designed to solve the given nonconvex problem by the mathematical program with equilibrium constraints (MPEC) and proximal-based strategy. We theoretically prove that the sequences generated by the designed algorithm converge to the nonconvex problem\u2019s local optimal solutions. Numerical experiment also demonstrates the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/sym13122393","type":"journal-article","created":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T01:29:33Z","timestamp":1639358973000},"page":"2393","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Proximal Algorithm with Convergence Guarantee for a Nonconvex Minimization Problem Based on Reproducing Kernel Hilbert Space"],"prefix":"10.3390","volume":"13","author":[{"given":"Hong-Xia","family":"Dou","sequence":"first","affiliation":[{"name":"School of Science, Xihua Univercity, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang-Jian","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, University of Electronic and Technology of China, Chengdu 611731, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1007\/s11075-019-00792-w","article-title":"Generation of point sets by convex optimization for interpolation in reproducing kernel Hilbert spaces","volume":"84","author":"Tanaka","year":"2020","journal-title":"Numer. 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