{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T10:01:58Z","timestamp":1770458518637,"version":"3.49.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2021,1,11]],"date-time":"2021-01-11T00:00:00Z","timestamp":1610323200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,11]],"date-time":"2021-01-11T00:00:00Z","timestamp":1610323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s12190-020-01461-1","type":"journal-article","created":{"date-parts":[[2021,1,11]],"date-time":"2021-01-11T19:26:26Z","timestamp":1610393186000},"page":"343-373","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Solving nonlinear monotone operator equations via modified SR1 update"],"prefix":"10.1007","volume":"67","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6142-3694","authenticated-orcid":false,"given":"Auwal Bala","family":"Abubakar","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7262-490X","authenticated-orcid":false,"given":"Jamilu","family":"Sabi\u2019u","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5463-4581","authenticated-orcid":false,"given":"Poom","family":"Kumam","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0337-1216","authenticated-orcid":false,"given":"Abdullah","family":"Shah","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,11]]},"reference":[{"issue":"5","key":"1461_CR1","doi-asserted-by":"publisher","first-page":"6760","DOI":"10.1007\/s40314-018-0712-5","volume":"37","author":"AB Abubakar","year":"2018","unstructured":"Abubakar, A.B., Kumam, P.: An improved three-term derivative-free method for solving nonlinear equations. Comput. Appl. Math. 37(5), 6760\u20136773 (2018)","journal-title":"Comput. Appl. Math."},{"issue":"1","key":"1461_CR2","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s11075-018-0541-z","volume":"81","author":"AB Abubakar","year":"2019","unstructured":"Abubakar, A.B., Kumam, P.: A descent dai-liao conjugate gradient method for nonlinear equations. Numer. Algorithm. 81(1), 197\u2013210 (2019)","journal-title":"Numer. Algorithm."},{"key":"1461_CR3","unstructured":"Abubakar, A.B., Kumam, P., Awwal, A.M.: A descent dai-liao projection method for convex constrained nonlinear monotone equations with applications. Thai J. Math. 17(1) (2018)"},{"issue":"8","key":"1461_CR4","doi-asserted-by":"publisher","first-page":"693","DOI":"10.3390\/math7080693","volume":"7","author":"AB Abubakar","year":"2019","unstructured":"Abubakar, A.B., Kumam, P., Awwal, A.M., Thounthong, P.: A modified self-adaptive conjugate gradient method for solving convex constrained monotone nonlinear equations for signal reovery problems. Mathematics 7(8), 693 (2019)","journal-title":"Mathematics"},{"key":"1461_CR5","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s40314-020-01151-5","volume":"39","author":"AB Abubakar","year":"2020","unstructured":"Abubakar, A.B., Kumam, P., Mohammad, H.: A note on the spectral gradient projection method for nonlinear monotone equations with applications. Comput. Appl. Math. 39, 129 (2020)","journal-title":"Comput. Appl. Math."},{"issue":"9","key":"1461_CR6","doi-asserted-by":"publisher","first-page":"767","DOI":"10.3390\/math7090767","volume":"7","author":"AB Abubakar","year":"2019","unstructured":"Abubakar, A.B., Kumam, P., Mohammad, H., Awwal, A.M.: An efficient conjugate gradient method for convex constrained monotone nonlinear equations with applications. Mathematics 7(9), 767 (2019)","journal-title":"Mathematics"},{"issue":"8","key":"1461_CR7","doi-asserted-by":"publisher","first-page":"745","DOI":"10.3390\/math7080745","volume":"7","author":"AB Abubakar","year":"2019","unstructured":"Abubakar, A.B., Kumam, P., Mohammad, H., Awwal, A.M., Kanokwan, S.: A modified Fletcher-Reeves conjugate gradient method for monotone nonlinear equations with some applications. Mathematics 7(8), 745 (2019)","journal-title":"Mathematics"},{"issue":"1","key":"1461_CR8","first-page":"501","volume":"18","author":"AB Abubakar","year":"2020","unstructured":"Abubakar, A.B., Rilwan, J., Yimer, S.E., Ibrahim, A.H., Ahmed, I.: Spectral three-term conjugate descent method for solving nonlinear monotone equations with convex constraints. Thai J. Math. 18(1), 501\u2013517 (2020)","journal-title":"Thai J. Math."},{"key":"1461_CR9","doi-asserted-by":"publisher","first-page":"158656","DOI":"10.1109\/ACCESS.2020.3020334","volume":"8","author":"S Aji","year":"2020","unstructured":"Aji, S., Kumam, P., Siricharoen, P., Abubakar, A.B., Yahaya, M.M.: A modified conjugate descent projection method for monotone nonlinear equations and image restoration. IEEE Access 8, 158656\u2013158665 (2020)","journal-title":"IEEE Access"},{"key":"1461_CR10","doi-asserted-by":"crossref","unstructured":"Babaie-Kafaki, S.: A modified scaled memoryless symmetric rank\u2013one method. Bollettino dell\u2019Unione Matematica Italiana, pp. 1\u201311 (2020)","DOI":"10.1007\/s40574-020-00231-y"},{"issue":"3","key":"1461_CR11","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1080\/10556788.2013.833199","volume":"29","author":"S Babaie-Kafaki","year":"2014","unstructured":"Babaie-Kafaki, S., Ghanbari, R.: A descent family of Dai\u2013Liao conjugate gradient methods. Optim. Methods Softw. 29(3), 583\u2013591 (2014)","journal-title":"Optim. Methods Softw."},{"issue":"2","key":"1461_CR12","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1137\/0801015","volume":"1","author":"Y Bing","year":"1991","unstructured":"Bing, Y., Lin, G.: An efficient implementation of merrills method for sparse or partially separable systems of nonlinear equations. SIAM J. Optim. 1(2), 206\u2013221 (1991)","journal-title":"SIAM J. Optim."},{"key":"1461_CR13","doi-asserted-by":"publisher","first-page":"101216","DOI":"10.1016\/j.najef.2020.101216","volume":"53","author":"Z Dai","year":"2020","unstructured":"Dai, Z., Dong, X., Kang, J., Hong, L.: Forecasting stock market returns: New technical indicators and two-step economic constraint method. North Am. J. Econ. Financ. 53, 101216 (2020)","journal-title":"North Am. J. Econ. Financ."},{"issue":"4","key":"1461_CR14","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":"1461_CR15","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."},{"key":"1461_CR16","doi-asserted-by":"crossref","unstructured":"Fukushima, M.: Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math. Program. 53(1-3), 99\u2013110 (1992)","DOI":"10.1007\/BF01585696"},{"issue":"1","key":"1461_CR17","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1109\/TPWRS.2015.2390037","volume":"31","author":"B Ghaddar","year":"2016","unstructured":"Ghaddar, B., Marecek, J., Mevissen, M.: Optimal power flow as a polynomial optimization problem. IEEE Trans. Power Syst. 31(1), 539\u2013546 (2016)","journal-title":"IEEE Trans. Power Syst."},{"issue":"1","key":"1461_CR18","first-page":"35","volume":"2","author":"WW Hager","year":"2006","unstructured":"Hager, W.W., Zhang, H.: A survey of nonlinear conjugate gradient methods. Pac. J. Optim. 2(1), 35\u201358 (2006)","journal-title":"Pac. J. Optim."},{"key":"1461_CR19","unstructured":"Ibrahim, A.H., Garba, A.I., Usman, H., Abubakar, J., Abubakar, A.B.: Derivative-free projection algorithm for nonlinear equations with convex constraints. Thai J. Math. 18(1) (2019)"},{"issue":"3","key":"1461_CR20","doi-asserted-by":"publisher","first-page":"e03466","DOI":"10.1016\/j.heliyon.2020.e03466","volume":"6","author":"AH Ibrahim","year":"2020","unstructured":"Ibrahim, A.H., Kumam, P., Abubakar, A.B., Jirakitpuwapat, W., Abubakar, J.: A hybrid conjugate gradient algorithm for constrained monotone equations with application in compressive sensing. Heliyon 6(3), e03466 (2020)","journal-title":"Heliyon"},{"issue":"9","key":"1461_CR21","first-page":"1959","volume":"21","author":"AH Ibrahim","year":"2020","unstructured":"Ibrahim, A.H., Kumam, P., Abubakar, A.B., Yusuf, U.B., Rilwan, J.: Derivative-free conjugate residual algorithms for convex constraints nonlinear monotone equations and signal recovery. J. Nonlinear Convex Anal. 21(9), 1959\u20131972 (2020)","journal-title":"J. Nonlinear Convex Anal."},{"issue":"4","key":"1461_CR22","doi-asserted-by":"publisher","first-page":"602","DOI":"10.3390\/math8040602","volume":"8","author":"AH Ibrahim","year":"2020","unstructured":"Ibrahim, A.H., Kumam, P., Abubakar, A.B., Abubakar, J., Muhammad, A.B.: Least-square-based three-term conjugate gradient projection method for $$\\ell _1$$-norm problems with application to compressed sensing. Mathematics 8(4), 602 (2020)","journal-title":"Mathematics"},{"issue":"1","key":"1461_CR23","doi-asserted-by":"publisher","first-page":"235","DOI":"10.3934\/math.2021016","volume":"6","author":"AH Ibrahim","year":"2020","unstructured":"Ibrahim, A.H., Kumam, P., Abubakar, A.B., Yusuf, U.B., Yimer, S.E., Aremu, K.O.: An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration. Aims Math. 6(1), 235\u2013260 (2020)","journal-title":"Aims Math."},{"issue":"3","key":"1461_CR24","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1080\/02331939708844339","volume":"41","author":"NA Iusem","year":"1997","unstructured":"Iusem, N.A., Solodov, V.M.: Newton-type methods with generalized distances for constrained optimization. Optimization 41(3), 257\u2013278 (1997)","journal-title":"Optimization"},{"key":"1461_CR25","doi-asserted-by":"crossref","unstructured":"Kaelo, P., Koorapetse, M.: A globally convergent projection method for a system of nonlinear monotone equations. Int. J. Comput. Math. 1\u201319 (2020)","DOI":"10.1007\/s40840-021-01171-2"},{"issue":"255","key":"1461_CR26","doi-asserted-by":"publisher","first-page":"1429","DOI":"10.1090\/S0025-5718-06-01840-0","volume":"75","author":"W La Cruz","year":"2006","unstructured":"La Cruz, W., Mart\u00ednez, J., Raydan, M.: Spectral residual method without gradient information for solving large-scale nonlinear systems of equations. Math. Comput. 75(255), 1429\u20131448 (2006)","journal-title":"Math. Comput."},{"issue":"4","key":"1461_CR27","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/0096-3003(87)90076-2","volume":"22","author":"K Meintjes","year":"1987","unstructured":"Meintjes, K., Morgan, A.P.: A methodology for solving chemical equilibrium systems. Appl. Math. Comput. 22(4), 333\u2013361 (1987)","journal-title":"Appl. Math. Comput."},{"key":"1461_CR28","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.apnum.2020.02.017","volume":"153","author":"J Sabi\u2019u","year":"2020","unstructured":"Sabi\u2019u, J., Shah, A., Waziri, M.Y.: Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations. Appl. Numer. Math. 153, 217\u2013233 (2020)","journal-title":"Appl. Numer. Math."},{"key":"1461_CR29","doi-asserted-by":"crossref","unstructured":"Solodov, M.V, Svaiter, B.F: A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, pp. 355\u2013369. Springer, Berlin (1998)","DOI":"10.1007\/978-1-4757-6388-1_18"},{"key":"1461_CR30","volume-title":"Optimization Theory and Methods: Nonlinear Programming","author":"W Sun","year":"1992","unstructured":"Sun, W., Yuan, Y.X.: Optimization Theory and Methods: Nonlinear Programming. Springer, Berlin (1992)"},{"key":"1461_CR31","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1016\/j.amc.2019.06.012","volume":"361","author":"MY Waziri","year":"2019","unstructured":"Waziri, M.Y., Ahmed, K., Sabiu, J.: A family of Hager-Zhang conjugate gradient methods for system of monotone nonlinear equations. Appl. Math. Comput. 361, 645\u2013660 (2019)","journal-title":"Appl. Math. Comput."},{"key":"1461_CR32","doi-asserted-by":"crossref","unstructured":"Waziri, M.Y., Hungu, K.A., Sabi\u2019u, J.: Descent Perry conjugate gradient methods for systems of monotone nonlinear equations. Numer. Algorithm., pp. 1\u201323 (2020)","DOI":"10.1007\/s11075-019-00836-1"},{"key":"1461_CR33","doi-asserted-by":"crossref","unstructured":"Waziri, M.Y., Ahmed, K., Sabi\u2019u, J.: A Dai-Liao conjugate gradient method via modified secant equation for system of nonlinear equations. Arab. J. Math., pp. 1\u201315 (2019)","DOI":"10.1007\/s40065-019-0264-6"},{"key":"1461_CR34","volume-title":"Power Generation, Operation, and Control","author":"AJ Wood","year":"2012","unstructured":"Wood, A.J., Wollenberg, B.F.: Power Generation, Operation, and Control. Wiley, New York (2012)"},{"issue":"1","key":"1461_CR35","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."},{"issue":"10","key":"1461_CR36","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.H., Liu, L.Y., Li, Z.H.: 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":"1461_CR37","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1023\/A:1021898630001","volume":"102","author":"JZ Zhang","year":"1999","unstructured":"Zhang, J.Z., Deng, N.Y., Chen, L.H.: New quasi-newton equation and related methods for unconstrained optimization. J. Optim. Theory Appl. 102(1), 147\u2013167 (1999)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"1461_CR38","doi-asserted-by":"publisher","first-page":"962","DOI":"10.1137\/S1052623499357957","volume":"11","author":"YB Zhao","year":"2001","unstructured":"Zhao, Y.B., Li, D.: Monotonicity of fixed point and normal mappings associated with variational inequality and its application. SIAM J. Optim. 11(4), 962\u2013973 (2001)","journal-title":"SIAM J. Optim."},{"key":"1461_CR39","doi-asserted-by":"crossref","unstructured":"Zheng, L., Yang, L., Liang, Y.: A modified spectral gradient projection method for solving non-linear monotone equations with convex constraints and its application. IEEE Access, pp. 92677\u201392686 (2020)","DOI":"10.1109\/ACCESS.2020.2990298"},{"key":"1461_CR40","first-page":"89","volume":"25","author":"W Zhou","year":"2007","unstructured":"Zhou, W., Li, D.: Limited memory bfgs method for nonlinear monotone equations. J. Comput. Math. 25, 89\u201396 (2007)","journal-title":"J. Comput. Math."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01461-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-020-01461-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01461-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,11]],"date-time":"2022-12-11T07:41:22Z","timestamp":1670744482000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-020-01461-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,11]]},"references-count":40,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1461"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01461-1","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,11]]},"assertion":[{"value":"13 August 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 November 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 November 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 January 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}