{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T07:16:42Z","timestamp":1758093402518,"version":"3.44.0"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T00:00:00Z","timestamp":1755043200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T00:00:00Z","timestamp":1755043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s10957-025-02820-3","type":"journal-article","created":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T16:35:58Z","timestamp":1755102958000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Modified Conjugate Gradient Projection Method for Constrained Monotone Equations with Applications"],"prefix":"10.1007","volume":"207","author":[{"given":"Yaping","family":"Hu","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,13]]},"reference":[{"issue":"6","key":"2820_CR1","doi-asserted-by":"publisher","first-page":"874","DOI":"10.3390\/sym12060874","volume":"12","author":"AM Awwal","year":"2020","unstructured":"Awwal, A.M., Wang, L., Kumam, P., Mohammad, H.: A two-step spectral gradient projection method for system of nonlinear monotone equations and image deblurring problems. Symmetry 12(6), 874 (2020)","journal-title":"Symmetry"},{"issue":"1","key":"2820_CR2","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"J Barzilai","year":"1988","unstructured":"Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8(1), 141\u2013148 (1988)","journal-title":"IMA J. Numer. Anal."},{"issue":"2","key":"2820_CR3","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1007\/s10589-013-9599-7","volume":"57","author":"X Cai","year":"2014","unstructured":"Cai, X., Gu, G., He, B.: On the O(1\/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators. Comput. Optim. Appl. 57(2), 339\u2013363 (2014)","journal-title":"Comput. Optim. Appl."},{"issue":"5","key":"2820_CR4","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1080\/10556780310001610493","volume":"18","author":"WL Cruz","year":"2003","unstructured":"Cruz, W.L., Raydan, M.: Nonmonotone spectral methods for large-scale nonlinear systems. Optim. Methods Softw. 18(5), 583\u2013599 (2003)","journal-title":"Optim. Methods Softw."},{"issue":"4","key":"2820_CR5","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1080\/10556789508805619","volume":"5","author":"SP Dirkse","year":"1995","unstructured":"Dirkse, S.P., Ferris, M.C.: MCPLIB: A collection of nonlinear mixed complementarity problems. Optim. Methods Softw. 5(4), 319\u2013345 (1995)","journal-title":"Optim. Methods Softw."},{"issue":"2","key":"2820_CR6","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201\u2013213 (2002)","journal-title":"Math. Program."},{"issue":"4","key":"2820_CR7","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1109\/MSP.2010.936726","volume":"27","author":"JA Fessler","year":"2010","unstructured":"Fessler, J.A.: Model-based image reconstruction for MRI. IEEE Signal Process. Mag. 27(4), 81\u201389 (2010)","journal-title":"IEEE Signal Process. Mag."},{"issue":"4","key":"2820_CR8","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1109\/JSTSP.2007.910281","volume":"1","author":"MA Figueiredo","year":"2008","unstructured":"Figueiredo, M.A., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1(4), 586\u2013597 (2008)","journal-title":"IEEE J. Sel. Top. Signal Process."},{"issue":"4","key":"2820_CR9","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/s10092-018-0291-2","volume":"55","author":"P Gao","year":"2018","unstructured":"Gao, P., He, C.: An efficient three-term conjugate gradient method for nonlinear monotone equations with convex constraints. Calcolo 55(4), 53 (2018)","journal-title":"Calcolo"},{"issue":"11","key":"2820_CR10","doi-asserted-by":"publisher","first-page":"2261","DOI":"10.1080\/00207160.2014.977879","volume":"92","author":"Y Hu","year":"2015","unstructured":"Hu, Y., Wei, Z.: Wei-Yao-Liu conjugate gradient projection algorithm for nonlinear monotone equations with convex constraints. Int. J. Comput. Math. 92(11), 2261\u20132272 (2015)","journal-title":"Int. J. Comput. Math."},{"issue":"2","key":"2820_CR11","first-page":"1241","volume":"189","author":"H Huang","year":"2007","unstructured":"Huang, H., Wei, Z., Yao, S.: The proof of the sufficient descent condition of the Wei-Yao-Liu congugate gradient method under the strong Wolfe-Powell line search. Appl. Math. Comput. 189(2), 1241\u20131245 (2007)","journal-title":"Appl. Math. Comput."},{"issue":"10","key":"2820_CR12","doi-asserted-by":"publisher","first-page":"2442","DOI":"10.1016\/j.camwa.2015.09.014","volume":"70","author":"J Liu","year":"2015","unstructured":"Liu, J., Li, S.: A projection method for convex constrained monotone nonlinear equations with applications. Comput. Math. Appl. 70(10), 2442\u20132453 (2015)","journal-title":"Comput. Math. Appl."},{"key":"2820_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.115006","volume":"424","author":"D Li","year":"2023","unstructured":"Li, D., Wu, J., Li, Y., Wang, S.: A modified spectral gradient projection-based algorithm for large-scale constrained nonlinear equations with applications in compressive sensing. J. Comput. Appl. Math. 424, 115006 (2023)","journal-title":"J. Comput. Appl. Math."},{"issue":"17","key":"2820_CR14","first-page":"7132","volume":"217","author":"S Lu","year":"2011","unstructured":"Lu, S., Wei, Z., Mo, L.: Some global convergence properties of the Wei-Yao-Liu conjugate gradient method with inexact line search. Appl. Math. Comput. 217(17), 7132\u20137137 (2011)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"2820_CR15","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1145\/78928.78930","volume":"16","author":"K Meintjes","year":"1990","unstructured":"Meintjes, K., Morgan, A.P.: Chemical equilibrium systems as numerical test problems. ACM Trans. Math. Soft. 16(2), 143\u2013151 (1990)","journal-title":"ACM Trans. Math. Soft."},{"key":"2820_CR16","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/978-1-4757-6388-1_18","volume-title":"Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods","author":"MV Solodov","year":"1998","unstructured":"Solodov, M.V., Svaiter, B.F.: A globally convergent inexact newton method for systems of monotone equations. In: Fukushima, M., Qi, L. (eds.) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, pp. 355\u2013369. Springer, Boston, MA (1998)"},{"issue":"2","key":"2820_CR17","first-page":"1341","volume":"183","author":"Z Wei","year":"2006","unstructured":"Wei, Z., Yao, S., Liu, L.: The convergence properties of some new conjugate gradient methods. Appl. Math. Comput. 183(2), 1341\u20131350 (2006)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"2820_CR18","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s10898-008-9324-8","volume":"44","author":"C Wang","year":"2009","unstructured":"Wang, C., Wang, Y.: A superlinearly convergent projection method for constrained systems of nonlinear equations. J. Global Optim. 44(2), 283\u2013296 (2009)","journal-title":"J. Global Optim."},{"key":"2820_CR19","volume-title":"Power Generations, Operations, and Control","author":"AJ Wood","year":"2013","unstructured":"Wood, A.J., Wollenberg, B.F., Shebl\u00e9, G.B.: Power Generations, Operations, and Control. Wiley, New York (2013)"},{"issue":"11","key":"2820_CR20","doi-asserted-by":"publisher","first-page":"3570","DOI":"10.1016\/j.na.2011.02.040","volume":"74","author":"Y Xiao","year":"2011","unstructured":"Xiao, Y., Wang, Q., Hu, Q.: Non-smooth equations based method for $$l_1$$-norm problems with applications to compressed sensing. Nonlinear Anal. Theor. 74(11), 3570\u20133577 (2011)","journal-title":"Nonlinear Anal. Theor."},{"issue":"1","key":"2820_CR21","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.jmaa.2013.04.017","volume":"405","author":"Y Xiao","year":"2013","unstructured":"Xiao, Y., Zhu, H.: A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing. J. Math. Anal. Appl. 405(1), 310\u2013319 (2013)","journal-title":"J. Math. Anal. Appl."},{"key":"2820_CR22","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.apnum.2019.08.022","volume":"147","author":"G Yuan","year":"2020","unstructured":"Yuan, G., Li, T., Hu, W.: A conjugate gradient algorithm for large-scale nonlinear equations and image restoration problems. Appl. Numer. Math. 147, 129\u2013141 (2020)","journal-title":"Appl. Numer. Math."},{"issue":"10","key":"2820_CR23","doi-asserted-by":"publisher","first-page":"2416","DOI":"10.1016\/j.apnum.2009.04.004","volume":"59","author":"Z Yu","year":"2009","unstructured":"Yu, Z., Lin, J., Sun, J., Xiao, Y., Liu, L., Li, Z.: Spectral gradient projection method for monotone nonlinear equations with convex constraints. Appl. Numer. Math. 59(10), 2416\u20132423 (2009)","journal-title":"Appl. Numer. Math."},{"issue":"1","key":"2820_CR24","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s10957-015-0781-1","volume":"168","author":"G Yuan","year":"2016","unstructured":"Yuan, G., Meng, Z., Li, Y.: A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations. J. Optim. Theory Appl. 168(1), 129\u2013152 (2016)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"2820_CR25","doi-asserted-by":"publisher","first-page":"117","DOI":"10.3934\/jimo.2013.9.117","volume":"9","author":"G Yu","year":"2013","unstructured":"Yu, G., Niu, S., Ma, J.: Multivariate spectral gradient projection method for nonlinear monotone equations with convex constraints. J. Ind. Manag. Optim. 9(1), 117\u2013129 (2013)","journal-title":"J. Ind. Manag. Optim."},{"issue":"14","key":"2820_CR26","first-page":"7616","volume":"219","author":"L Zhang","year":"2013","unstructured":"Zhang, L., Jian, S.: Further studies on the Wei-Yao-Liu nonlinear conjugate gradient method. Appl. Math. Comput. 219(14), 7616\u20137621 (2013)","journal-title":"Appl. Math. Comput."},{"issue":"2","key":"2820_CR27","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1016\/j.cam.2005.10.002","volume":"196","author":"L Zhang","year":"2006","unstructured":"Zhang, L., Zhou, W.: Spectral gradient projection method for solving nonlinear monotone equations. J. Comput. Appl. Math. 196(2), 478\u2013484 (2006)","journal-title":"J. Comput. Appl. Math."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-025-02820-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-025-02820-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-025-02820-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T07:44:25Z","timestamp":1758008665000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-025-02820-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,13]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["2820"],"URL":"https:\/\/doi.org\/10.1007\/s10957-025-02820-3","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2025,8,13]]},"assertion":[{"value":"17 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 August 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"54"}}