{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:46:25Z","timestamp":1740123985705,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,9,26]],"date-time":"2019-09-26T00:00:00Z","timestamp":1569456000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,9,26]],"date-time":"2019-09-26T00:00:00Z","timestamp":1569456000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Ministry of Science and Education of Russia","award":["1.460.2016\/1.4"],"award-info":[{"award-number":["1.460.2016\/1.4"]}]},{"name":"Russian Foundation for Basic Research","award":["19-01-00431"],"award-info":[{"award-number":["19-01-00431"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2020,2]]},"DOI":"10.1007\/s10957-019-01589-6","type":"journal-article","created":{"date-parts":[[2019,9,26]],"date-time":"2019-09-26T06:02:15Z","timestamp":1569477735000},"page":"534-546","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Non-monotone Conjugate Subgradient Type Method for Minimization of Convex Functions"],"prefix":"10.1007","volume":"184","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9426-6314","authenticated-orcid":false,"given":"Igor","family":"Konnov","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,26]]},"reference":[{"key":"1589_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82118-9","volume-title":"Minimization Methods for Non-differentiable Functions","author":"NZ Shor","year":"1985","unstructured":"Shor, N.Z.: Minimization Methods for Non-differentiable Functions. Springer, Berlin (1985)"},{"key":"1589_CR2","volume-title":"Introduction to Optimization","author":"BT Polyak","year":"1987","unstructured":"Polyak, B.T.: Introduction to Optimization. Optimization Software, New York (1987)"},{"key":"1589_CR3","doi-asserted-by":"publisher","DOI":"10.1142\/1493","volume-title":"Nonsmooth Optimization","author":"MM M\u00e4kela","year":"1992","unstructured":"M\u00e4kela, M.M., Neittaanm\u00e4ki, P.: Nonsmooth Optimization. World Scientific, Singapore (1992)"},{"key":"1589_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0074500","volume-title":"Methods of Descent for Nondifferentiable Optimization","author":"KC Kiwiel","year":"1985","unstructured":"Kiwiel, K.C.: Methods of Descent for Nondifferentiable Optimization. Springer, Berlin (1985)"},{"key":"1589_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex Analysis and Minimization Algorithms","author":"JB Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.B., Lemar\u00e9chal, C.: Convex Analysis and Minimization Algorithms. Springer, Berlin (1993)"},{"key":"1589_CR6","volume-title":"Nonlinear Optimization and Variational Inequalities","author":"IV Konnov","year":"2013","unstructured":"Konnov, I.V.: Nonlinear Optimization and Variational Inequalities. Kazan University Press, Kazan (2013). [in Russian]"},{"key":"1589_CR7","doi-asserted-by":"crossref","unstructured":"Wolfe,\u00a0P.: A method of conjugate subgradients for minimizing nondifferentiable functions. In: Balinski,\u00a0M.L., Wolfe,\u00a0P. (eds.) Nondifferentiable Optimization. Mathematical Programming Study 3, 145\u2013173 (1975)","DOI":"10.1007\/BFb0120703"},{"key":"1589_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12603-5","volume-title":"Nondifferentiable Optimization","author":"VF Dem\u2019yanov","year":"1985","unstructured":"Dem\u2019yanov, V.F., Vasil\u2019yev, L.V.: Nondifferentiable Optimization. Optimization Software, New York (1985)"},{"key":"1589_CR9","first-page":"68","volume":"3","author":"ND Chepurnoi","year":"1982","unstructured":"Chepurnoi, N.D.: Relaxation method of minimization of convex functions. Dokl. Akad. Nauk Ukrainy. Ser. A. 3, 68\u201369 (1982). [in Russian]","journal-title":"Dokl. Akad. Nauk Ukrainy. Ser. A."},{"key":"1589_CR10","unstructured":"Konnov,\u00a0I.V.: A subgradient method of successive relaxation for solving optimization problems. Preprint VINITI No. 531-83, Faculty of Computational Mathematics and Cybernetics, Kazan University, Kazan, 14 pp. (1982). [in Russian]"},{"key":"1589_CR11","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1007\/BF02591907","volume":"27","author":"KC Kiwiel","year":"1983","unstructured":"Kiwiel, K.C.: An aggregate subgradient method for nonsmooth convex minimization. Math. Program. 27, 320\u2013341 (1983)","journal-title":"Math. Program."},{"key":"#cr-split#-1589_CR12.1","unstructured":"Konnov, I.V.: A method of the conjugate subgradient type for minimization of functionals. Issled. Prikl. Matem. 12, 59-62 (1984)"},{"key":"#cr-split#-1589_CR12.2","unstructured":"Engl. transl.: J. Soviet Math. 45, 1026-1029 (1989)"},{"key":"1589_CR13","volume-title":"Methods of Nonconvex Optimization","author":"VS Mikhalevich","year":"1987","unstructured":"Mikhalevich, V.S., Gupal, A.M., Norkin, V.I.: Methods of Nonconvex Optimization. Nauka, Moscow (1987). [in Russian]"},{"key":"1589_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56886-2","volume-title":"Combined Relaxation Methods for Variational Inequalities","author":"IV Konnov","year":"2001","unstructured":"Konnov, I.V.: Combined Relaxation Methods for Variational Inequalities. Springer, Berlin (2001)"},{"key":"1589_CR15","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1007\/BF01069305","volume":"14","author":"AM Gupal","year":"1978","unstructured":"Gupal, A.M.: Methods of minimizing functions that satisfy a Lipschitz condition, averaging the directions of descent. Cybernetics 14, 695\u2013698 (1978)","journal-title":"Cybernetics"},{"key":"1589_CR16","first-page":"131","volume":"6","author":"ND Chepurnoi","year":"1981","unstructured":"Chepurnoi, N.D.: A method of average quasigradients with stepwise step control for minimization of weakly convex functions. Kibernetika 6, 131\u2013132 (1981). [in Russian]","journal-title":"Kibernetika"},{"key":"1589_CR17","doi-asserted-by":"publisher","first-page":"82","DOI":"10.3103\/S1066369X18010127","volume":"62","author":"IV Konnov","year":"2018","unstructured":"Konnov, I.V.: Conditional gradient method without line-search. Russ. Mathem. (Izv. VUZ.) 62, 82\u201385 (2018)","journal-title":"Russ. Mathem. (Izv. VUZ.)"},{"key":"1589_CR18","first-page":"353","volume":"20","author":"IV Konnov","year":"2018","unstructured":"Konnov, I.V.: A simple adaptive step-size choice for iterative optimization methods. Adv. Model. Optim. 20, 353\u2013369 (2018)","journal-title":"Adv. Model. Optim."},{"key":"1589_CR19","doi-asserted-by":"publisher","first-page":"2275","DOI":"10.1080\/02331934.2018.1530235","volume":"67","author":"IV Konnov","year":"2018","unstructured":"Konnov, I.V.: Simplified versions of the conditional gradient method. Optimization 67, 2275\u20132290 (2018)","journal-title":"Optimization"},{"key":"1589_CR20","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BFb0120700","volume-title":"Nondifferentiable Optimization","author":"C. Lemarechal","year":"1975","unstructured":"Lemar\u00e9chal,\u00a0C.: An extension of Davidon methods to nondifferentiable problems. In: Balinski,\u00a0M.L., Wolfe,\u00a0P. (eds.) Nondifferentiable Optimization. Mathematical Programming Study 3, pp. 95\u2013109 (1975)"},{"key":"1589_CR21","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"1589_CR22","volume-title":"Numerical Methods in Extremal Problems","author":"BN Pshenichnyi","year":"1978","unstructured":"Pshenichnyi, B.N., Danilin, Y.M.: Numerical Methods in Extremal Problems. MIR, Moscow (1978)"},{"key":"1589_CR23","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1007\/BF01069138","volume":"8","author":"NZ Shor","year":"1972","unstructured":"Shor, N.Z., Shabashova, L.P.: Solution of minimax problems by the method of generalized gradient descent with dilatation of the space. Cybernetics 8, 88\u201394 (1972)","journal-title":"Cybernetics"},{"key":"1589_CR24","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/s10107-007-0149-x","volume":"120","author":"Y Nesterov","year":"2009","unstructured":"Nesterov, Y.: Primal\u2013dual subgradient methods for convex problems. Math. Program. 120, 261\u2013283 (2009)","journal-title":"Math. Program."},{"key":"1589_CR25","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1007\/s10957-014-0677-5","volume":"165","author":"Y Nesterov","year":"2015","unstructured":"Nesterov, Y., Shikhman, V.: Quasi-monotone subgradient methods for nonsmooth convex minimization. J. Optim. Theory Appl. 165, 917\u2013940 (2015)","journal-title":"J. Optim. Theory Appl."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-019-01589-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-019-01589-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-019-01589-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T23:07:26Z","timestamp":1664492846000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-019-01589-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,26]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,2]]}},"alternative-id":["1589"],"URL":"https:\/\/doi.org\/10.1007\/s10957-019-01589-6","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2019,9,26]]},"assertion":[{"value":"20 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 September 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}