{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T07:46:17Z","timestamp":1768203977776,"version":"3.49.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T00:00:00Z","timestamp":1750464000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T00:00:00Z","timestamp":1750464000000},"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":["Optim Lett"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s11590-025-02215-3","type":"journal-article","created":{"date-parts":[[2025,6,21]],"date-time":"2025-06-21T00:28:46Z","timestamp":1750465726000},"page":"143-161","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Expected value method for a class of stochastic linear circular cone complementarity problems"],"prefix":"10.1007","volume":"20","author":[{"given":"Kaiyuan","family":"Guan","sequence":"first","affiliation":[]},{"given":"Jingyong","family":"Tang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,21]]},"reference":[{"key":"2215_CR1","doi-asserted-by":"publisher","first-page":"211","DOI":"10.3934\/naco.2015.5.211","volume":"5","author":"YQ Bai","year":"2015","unstructured":"Bai, Y.Q., Gao, X.R., Wang, G.Q.: Primal-dual interior-point algorithms for convex quadratic circular cone optimization. Numer. Algebra Control Optim. 5, 211\u2013231 (2015)","journal-title":"Numer. Algebra Control Optim."},{"key":"2215_CR2","doi-asserted-by":"publisher","first-page":"739","DOI":"10.3934\/jimo.2016.12.739","volume":"12","author":"YQ Bai","year":"2016","unstructured":"Bai, Y.Q., Ma, P.F., Zhang, J.: A polynomial-time interior-point method for circular cone programming based on kernel functions. J. Ind. Manag. Optim. 12, 739\u2013756 (2016)","journal-title":"J. Ind. Manag. Optim."},{"issue":"6","key":"2215_CR3","doi-asserted-by":"publisher","first-page":"1117","DOI":"10.1109\/TRO.2007.910774","volume":"23","author":"SP Boyd","year":"2007","unstructured":"Boyd, S.P., Wegbreit, B.: Fast computation of optimal contact forces. IEEE Tran. Robot. 23(6), 1117\u20131132 (2007)","journal-title":"IEEE Tran. Robot."},{"key":"2215_CR4","doi-asserted-by":"publisher","first-page":"1022","DOI":"10.1287\/moor.1050.0160","volume":"30","author":"X Chen","year":"2005","unstructured":"Chen, X., Fukushima, M.: Expected residual minimization method for stochastic linear complementarity problems. Math. Oper. Res. 30, 1022\u20131038 (2005)","journal-title":"Math. Oper. Res."},{"issue":"2","key":"2215_CR5","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1137\/070702187","volume":"20","author":"X Chen","year":"2009","unstructured":"Chen, X., Zhang, C.: Smoothing projected gradient method and its application to stochastic linear complementarity problems. SIAM J. Optim. 20(2), 627\u2013649 (2009)","journal-title":"SIAM J. Optim."},{"issue":"12","key":"2215_CR6","doi-asserted-by":"publisher","first-page":"2227","DOI":"10.1080\/02331934.2016.1217861","volume":"65","author":"XN Chi","year":"2016","unstructured":"Chi, X.N., Wan, Z.P., Zhu, Z.B., Yuan, L.Y.: A nonmonotone smoothing Newton method for circular cone programming. Optim. 65(12), 2227\u20132250 (2016)","journal-title":"Optim."},{"issue":"5","key":"2215_CR7","doi-asserted-by":"publisher","first-page":"1262","DOI":"10.1016\/S0252-9602(17)30072-3","volume":"37B","author":"XN Chi","year":"2017","unstructured":"Chi, X.N., Wei, H.J., Wan, Z.P., Zhu, Z.B.: Smoothing Newton algorithm for the circular cone programming with a nonmonotone line search. Acta Math. Scientia 37B(5), 1262\u20131280 (2017)","journal-title":"Acta Math. Scientia"},{"key":"2215_CR8","first-page":"146","volume":"26","author":"XN Chi","year":"2019","unstructured":"Chi, X.N., Wei, H.J., Wan, Z.P., Zhu, Z.B.: A nonmonotone smoothing Newton algorithm for circular cone complementarity problems. J. Comput. Anal. Appl. 26, 146\u2013162 (2019)","journal-title":"J. Comput. Anal. Appl."},{"key":"2215_CR9","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.laa.2004.03.028","volume":"393","author":"MS Gowda","year":"2004","unstructured":"Gowda, M.S., Sznajder, R., Tao, J.: Some P-properties for linear transformations on Euclidean Jordan algebras. Linear Algebra Appl. 393, 203\u2013232 (2004)","journal-title":"Linear Algebra Appl."},{"key":"2215_CR10","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/s101070050024","volume":"84","author":"G G\u00fcrkan","year":"1999","unstructured":"G\u00fcrkan, G., \u00d6zge, A.Y., Robinson, S.M.: Sample-path solution of stochastic variational inequalities. Math. Program. 84, 313\u2013333 (1999)","journal-title":"Math. Program."},{"issue":"3","key":"2215_CR11","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s11075-013-9803-y","volume":"67","author":"YK Huang","year":"2014","unstructured":"Huang, Y.K., Liu, H.W., Zhou, S.: A Barzilai-Borwein type method for stochastic linear complementarity problems. Numer. Algor. 67(3), 477\u2013489 (2014)","journal-title":"Numer. Algor."},{"issue":"5","key":"2215_CR12","doi-asserted-by":"publisher","first-page":"6795","DOI":"10.1007\/s40314-018-0687-2","volume":"37","author":"YF Ke","year":"2018","unstructured":"Ke, Y.F., Ma, C.F., Zhang, H.: The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems. Comput. Appl. Math. 37(5), 6795\u20136820 (2018)","journal-title":"Comput. Appl. Math."},{"issue":"2","key":"2215_CR13","doi-asserted-by":"publisher","first-page":"171","DOI":"10.3934\/naco.2017011","volume":"7","author":"B Kheirfam","year":"2017","unstructured":"Kheirfam, B., Wang, G.Q.: An infeasible full NT-step interior point method for circular optimization. Numer. Algebra Control Optim. 7(2), 171\u2013184 (2017)","journal-title":"Numer. Algebra Control Optim."},{"key":"2215_CR14","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s11590-006-0037-y","volume":"1","author":"L Kong","year":"2007","unstructured":"Kong, L., Xiu, N.: New smooth C-functions for symmetric cone complementarity problems. Optim. Let. 1, 391\u2013400 (2007)","journal-title":"Optim. Let."},{"key":"2215_CR15","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1080\/02331934.2015.1062008","volume":"65","author":"N Kreji\u0107","year":"2016","unstructured":"Kreji\u0107, N., Jerinki\u0107, N.K., Rapaji\u0107, S.: Barzilai-Borwein method with variable sample size for stochastic linear complementarity problems. Optimization 65, 479\u2013499 (2016)","journal-title":"Optimization"},{"issue":"8","key":"2215_CR16","first-page":"1460","volume":"25","author":"Z Li","year":"2014","unstructured":"Li, Z., Ge, S.S., Liu, S.B.: Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks. IEEE Tran. Neural. Networ. 25(8), 1460\u20131473 (2014)","journal-title":"IEEE Tran. Neural. Networ."},{"key":"2215_CR17","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s10107-017-1121-z","volume":"165","author":"GH Lin","year":"2017","unstructured":"Lin, G.H., Luo, M.J., Zhang, D., Zhang, J.: Stochastic second-order-cone complementarity problems: expected residual minimization formulation and its applications. Math. Program. 165, 197\u2013233 (2017)","journal-title":"Math. Program."},{"issue":"7","key":"2215_CR18","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1080\/01630563.2017.1300172","volume":"38","author":"MJ Luo","year":"2017","unstructured":"Luo, M.J., Zhang, Y., Li, Y.J.: Expected value and sample average approximation method for solving stochastic second-order cone complementarity problems. Numer. Func. Anal. Optim. 38(7), 911\u2013925 (2017)","journal-title":"Numer. Func. Anal. Optim."},{"issue":"2","key":"2215_CR19","first-page":"225","volume":"17","author":"PF Ma","year":"2016","unstructured":"Ma, P.F., Bai, Y.Q., Chen, J.-S.: A self-concordant interior point algorithm for nonsymmetric circular cone programming. J. Nonlinear Convex Anal. 17(2), 225\u2013241 (2016)","journal-title":"J. Nonlinear Convex Anal."},{"key":"2215_CR20","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/s10589-015-9781-1","volume":"63","author":"XH Miao","year":"2016","unstructured":"Miao, X.H., Guo, S.J., Qi, N., Chen, J.S.: Constructions of complementarity functions and merit functions for circular cone complementarity problem. Comput. Optim. Appl. 63, 495\u2013522 (2016)","journal-title":"Comput. Optim. Appl."},{"key":"2215_CR21","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.amc.2015.07.064","volume":"269","author":"XH Miao","year":"2015","unstructured":"Miao, X.H., Yang, J.T., Hu, S.L.: A generalized Newton method for absolute value equations associated with circular cones. Appl. Math. Comput. 269, 155\u2013168 (2015)","journal-title":"Appl. Math. Comput."},{"key":"2215_CR22","volume-title":"Probability and Measure","author":"B Patrick","year":"1995","unstructured":"Patrick, B.: Probability and Measure. Wiley, New York (1995)"},{"issue":"3","key":"2215_CR23","doi-asserted-by":"publisher","first-page":"1103","DOI":"10.1007\/s13160-018-0317-9","volume":"35","author":"M Pirhaji","year":"2018","unstructured":"Pirhaji, M., Zangiabadi, M., Mansouri, H.: A path following interior-point method for linear complementarity problems over circular cones. Japan J. Indus. Appl. Math. 35(3), 1103\u20131121 (2018)","journal-title":"Japan J. Indus. Appl. Math."},{"issue":"2","key":"2215_CR24","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s40305-018-0225-3","volume":"7","author":"G Sun","year":"2019","unstructured":"Sun, G., Zhang, J., Yu, L.Y., Lin, G.H.: A new complementarity function and applications in stochastic second-order cone complementarity problems. J. Oper. Res. Soc. China. 7(2), 251\u2013283 (2019)","journal-title":"J. Oper. Res. Soc. China."},{"issue":"2","key":"2215_CR25","first-page":"261","volume":"16","author":"G Sun","year":"2020","unstructured":"Sun, G., Yu, L.Y., Lin, G.H., Dong, X.D.: A class of stochastic second-order-cone complementarity problems. Pac. J. Optim. 16(2), 261\u2013287 (2020)","journal-title":"Pac. J. Optim."},{"key":"2215_CR26","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1007\/s10479-020-03773-8","volume":"295","author":"JY Tang","year":"2020","unstructured":"Tang, J.Y., Zhou, J.C.: Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones. Ann. Oper. Res. 295, 787\u2013808 (2020)","journal-title":"Ann. Oper. Res."},{"issue":"7","key":"2215_CR27","doi-asserted-by":"publisher","first-page":"2005","DOI":"10.1080\/02331934.2020.1847108","volume":"71","author":"JY Tang","year":"2022","unstructured":"Tang, J.Y., Zhou, J.C.: Improved convergence analysis of a smoothing Newton method for the circular cone programming. Optimization 71(7), 2005\u20132031 (2022)","journal-title":"Optimization"},{"key":"2215_CR28","doi-asserted-by":"publisher","first-page":"209","DOI":"10.21136\/AM.2021.0129-20","volume":"67","author":"J Tang","year":"2022","unstructured":"Tang, J., Chen, Y.: Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems. Appl. Math. 67, 209\u2013231 (2022)","journal-title":"Appl. Math."},{"issue":"2","key":"2215_CR29","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/j.ejor.2017.09.008","volume":"265","author":"GX Wang","year":"2018","unstructured":"Wang, G.X., Zhang, J., Zeng, B., Lin, G.H.: Expected residual minimization formulation for a class of stochastic linear second-order cone complementarity problems. Eur. J. Oper. Res. 265(2), 437\u2013447 (2018)","journal-title":"Eur. J. Oper. Res."},{"key":"2215_CR30","first-page":"807","volume":"14","author":"JC Zhou","year":"2013","unstructured":"Zhou, J.C., Chen, J.S.: Properties of circular cone and spectral factorization associated with circular cone. J. Nonlinear Convex Anal. 14, 807\u2013816 (2013)","journal-title":"J. Nonlinear Convex Anal."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-025-02215-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-025-02215-3","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-025-02215-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T04:19:38Z","timestamp":1768191578000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-025-02215-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,21]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["2215"],"URL":"https:\/\/doi.org\/10.1007\/s11590-025-02215-3","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,21]]},"assertion":[{"value":"9 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}