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Applying the obtained results to nonconvex regularization problems with SCAD, MCP and <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\ell _p$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mi>p<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> penalty (<jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$0\\le p \\le 1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>0<\/mml:mn>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mi>p<\/mml:mi>\n                    <mml:mo>\u2264<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>) and utilizing the recovery bound theory, we establish the convergence of their proximal gradient algorithms to an approximate global solution of nonconvex regularization problems. The established results include the existing convergence theory for <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\ell _1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> or <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\ell _0$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>\u2113<\/mml:mi>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> regularization problems for finding a true sparse solution as special cases. Preliminary numerical results show that our proposed algorithms can find approximate true sparse solutions that are much better than stationary solutions that are found by using the standard proximal gradient algorithm.<\/jats:p>","DOI":"10.1007\/s10107-024-02068-1","type":"journal-article","created":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T13:02:21Z","timestamp":1709730141000},"page":"181-206","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On convergence of iterative thresholding algorithms to approximate sparse solution for composite nonconvex optimization"],"prefix":"10.1007","volume":"211","author":[{"given":"Yaohua","family":"Hu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xinlin","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5583-4032","authenticated-orcid":false,"given":"Xiaoqi","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,3,6]]},"reference":[{"key":"2068_CR1","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1214\/08-AOS620","volume":"37","author":"PJ Bickel","year":"2009","unstructured":"Bickel, P.J., Ritov, Y., Tsybakov, A.B.: Simultaneous analysis of Lasso and Dantzig selector. 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