{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:46:48Z","timestamp":1765039608994,"version":"3.37.3"},"reference-count":74,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T00:00:00Z","timestamp":1651622400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T00:00:00Z","timestamp":1651622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["20-71-10032"],"award-info":[{"award-number":["20-71-10032"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2022,7]]},"DOI":"10.1007\/s10589-022-00374-y","type":"journal-article","created":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T08:02:52Z","timestamp":1651651372000},"page":"649-671","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["DC Semidefinite programming and cone constrained DC optimization I: theory"],"prefix":"10.1007","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0677-0797","authenticated-orcid":false,"given":"M. V.","family":"Dolgopolik","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,4]]},"reference":[{"key":"374_CR1","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"PA Absil","year":"2009","unstructured":"Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2009)"},{"key":"374_CR2","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10107-002-0339-5","volume":"95","author":"F Alizadeh","year":"2003","unstructured":"Alizadeh, F., Goldfarb, D.: Second-order cone programming. Math. Program. 95, 3\u201351 (2003)","journal-title":"Math. Program."},{"key":"374_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718829","volume-title":"Lectures on Modern Convex Optimization. Analysis, Algorithms, and Engineering Applications","author":"A Ben-Tal","year":"2001","unstructured":"Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization. Analysis, Algorithms, and Engineering Applications. SIAM, Philadelphia (2001)"},{"key":"374_CR4","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/BF00150866","volume":"60","author":"G Bianchi","year":"1996","unstructured":"Bianchi, G., Colesanti, A., Pucci, C.: On the second differentiability of convex surfaces. Geom. Dedicata. 60, 39\u201348 (1996)","journal-title":"Geom. Dedicata."},{"key":"374_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems","author":"JF Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)"},{"key":"374_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"374_CR7","doi-asserted-by":"publisher","first-page":"1322","DOI":"10.1080\/10556788.2018.1506452","volume":"34","author":"A Canelas","year":"2019","unstructured":"Canelas, A., Carrasco, M., L\u00f3pez, J.: A feasible direction algorithm for nonlinear second-order cone programs. Optim. Meth. Softw. 34, 1322\u20131341 (2019)","journal-title":"Optim. Meth. Softw."},{"key":"374_CR8","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1137\/19M1303320","volume":"31","author":"R Correa","year":"2021","unstructured":"Correa, R., L\u00f3pez, M.A., P\u00e9rez-Aros, P.: Necessary and sufficient optimality conditions in DC semi-infinite programming. SIAM J. Optim. 31, 837\u2013865 (2021)","journal-title":"SIAM J. Optim."},{"key":"374_CR9","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/s10898-019-00755-4","volume":"75","author":"W de Oliveira","year":"2019","unstructured":"de Oliveira, W.: Proximal bundle methods for nonsmooth DC programming. J. Glob. Optim. 75, 523\u2013563 (2019)","journal-title":"J. Glob. Optim."},{"key":"374_CR10","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1007\/s11228-018-0497-0","volume":"27","author":"W de Oliveira","year":"2019","unstructured":"de Oliveira, W., Tcheou, M.P.: An inertial algorithm for DC programming. Set-Valued Var. Anal. 27, 895\u2013919 (2019)","journal-title":"Set-Valued Var. Anal."},{"key":"374_CR11","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1006\/jmaa.1997.5745","volume":"217","author":"M D\u00fcr","year":"1998","unstructured":"D\u00fcr, M., Horst, R., Locatelli, M.: Necessary and sufficient global optimality conditions for convex maximization revisited. J. Math. Anal. Appl. 217, 637\u2013649 (1998)","journal-title":"J. Math. Anal. Appl."},{"key":"374_CR12","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0895479895290954","volume":"20","author":"A Edelman","year":"1998","unstructured":"Edelman, A., Tom\u00e1s, A.A., Smith, T.S.: The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20, 303\u2013353 (1998)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"374_CR13","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1007\/s10898-008-9343-5","volume":"43","author":"A Ferrer","year":"2009","unstructured":"Ferrer, A., Mart\u00ednez-Legaz, J.E.: Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function. J. Glob. Optim. 43, 513\u2013531 (2009)","journal-title":"J. Glob. Optim."},{"key":"374_CR14","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10898-019-00742-9","volume":"74","author":"NA Gadhi","year":"2019","unstructured":"Gadhi, N.A.: Necessary optimality conditions for a nonsmooth semi-infinite programming problem. J. Glob. Optim. 74, 161\u2013168 (2019)","journal-title":"J. Glob. Optim."},{"key":"374_CR15","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s10898-017-0568-z","volume":"71","author":"M Gaudioso","year":"2018","unstructured":"Gaudioso, M., Giallombardo, G., Miglionico, G., Bagirov, A.M.: Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations. J. Glob. Optim. 71, 37\u201355 (2018)","journal-title":"J. Glob. Optim."},{"key":"374_CR16","doi-asserted-by":"crossref","unstructured":"Goberna, M.A., L\u00f3pez, M.A. (eds.): Semi-Infinite Programming: Recent Advances. Kluwer Academic Publishers, Dordrecht (2001)","DOI":"10.1007\/978-1-4757-3403-4"},{"key":"374_CR17","doi-asserted-by":"publisher","first-page":"1079","DOI":"10.1002\/(SICI)1099-1239(199611)6:9\/10<1079::AID-RNC270>3.0.CO;2-#","volume":"6","author":"KC Goh","year":"1996","unstructured":"Goh, K.C., Safonov, M.G., Ly, J.H.: Robust synthesis via bilinear matrix inequalities. Int. J. Robust Nonlinear Control 6, 1079\u20131095 (1996)","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"374_CR18","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/BF01099648","volume":"7","author":"KC Goh","year":"1995","unstructured":"Goh, K.C., Safonov, M.G., Papavassilopous, G.P.: Global optimization for the Biaffine Matrix Inequality problem. J. Glob. Optim. 7, 365\u2013380 (1995)","journal-title":"J. Glob. Optim."},{"key":"374_CR19","doi-asserted-by":"publisher","first-page":"707","DOI":"10.2140\/pjm.1959.9.707","volume":"9","author":"P Hartman","year":"1959","unstructured":"Hartman, P.: On functions representable as a difference of convex functions. Pac. J. Math. 9, 707\u2013713 (1959)","journal-title":"Pac. J. Math."},{"key":"374_CR20","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/S0167-6911(99)00049-3","volume":"38","author":"D Henrion","year":"1999","unstructured":"Henrion, D., Tarbouriech, S., \u0160ebek, M.: Rank-one LMI approach to simultaneous stabilization of linear systems. Syst. Control Lett. 38, 79\u201389 (1999)","journal-title":"Syst. Control Lett."},{"key":"374_CR21","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/978-3-642-45610-7_3","volume-title":"Convexity and Duality in Optimization","author":"JB Hiriart-Urruty","year":"1985","unstructured":"Hiriart-Urruty, J.B.: Generalized differentiability\/duality and optimization for problems dealing with differences of convex functions. In: Ponstein, J. (ed.) Convexity and Duality in Optimization, pp. 37\u201370. Springer, Berlin (1985)"},{"key":"374_CR22","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/978-1-4757-6019-4_13","volume-title":"Nonsmooth Optimization and Related Topics","author":"JB Hiriart-Urruty","year":"1989","unstructured":"Hiriart-Urruty, J.B.: From convex optimization to nonconvex optimization. Necessary and sufficient conditions for global optimality. In: Clarke, F.H., Dem\u2019yanov, V.F., Giannessi, F. (eds.) Nonsmooth Optimization and Related Topics, pp. 219\u2013239. Springer, Boston (1989)"},{"key":"374_CR23","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1023\/A:1008365206132","volume":"13","author":"JB Hiriart-Urruty","year":"1998","unstructured":"Hiriart-Urruty, J.B.: Conditions for global optimality 2. J. Glob. Optim. 13, 349\u2013367 (1998)","journal-title":"J. Glob. Optim."},{"key":"374_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/A:1021765131316","volume":"103","author":"R Horst","year":"1999","unstructured":"Horst, R., Thoai, N.V.: DC programming: overview. J. Optim. Theory Appl. 103, 1\u201343 (1999)","journal-title":"J. Optim. Theory Appl."},{"key":"374_CR25","volume-title":"Theory of Extremal Problems","author":"AD Ioffe","year":"1979","unstructured":"Ioffe, A.D., Tihomirov, V.M.: Theory of Extremal Problems. North-Holland, Amsterdam (1979)"},{"key":"374_CR26","doi-asserted-by":"publisher","first-page":"1892","DOI":"10.1137\/16M1115733","volume":"28","author":"K Joki","year":"2018","unstructured":"Joki, K., Bagirov, A.M., Karmitsa, N., M\u00e4kel\u00e4, M., Taheri, S.: Double bundle method for finding Clarke stationary points in nonsmooth DC programming. SIAM J. Optim. 28, 1892\u20131919 (2018)","journal-title":"SIAM J. Optim."},{"key":"374_CR27","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1090\/S0002-9939-1951-0042064-2","volume":"2","author":"RV Kadison","year":"1951","unstructured":"Kadison, R.V.: Order properties of bounded self-adjoint operators. Proc. Am. Math. Soc. 2, 505\u2013510 (1951)","journal-title":"Proc. Am. Math. Soc."},{"key":"374_CR28","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1007\/s10898-010-9561-5","volume":"49","author":"N Kanzi","year":"2011","unstructured":"Kanzi, N.: Necessary optimality conditions for nonsmooth semi-infinite programming problems. J. Glob. Optim. 49, 713\u2013725 (2011)","journal-title":"J. Glob. Optim."},{"key":"374_CR29","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s11590-006-0009-2","volume":"1","author":"H Kato","year":"2007","unstructured":"Kato, H., Fukushima, M.: An SQP-type algorithm for nonlinear second-order cone programs. Optim. Lett. 1, 129\u2013144 (2007)","journal-title":"Optim. Lett."},{"key":"374_CR30","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1080\/1055678031000098773","volume":"18","author":"M Ko\u010dvara","year":"2003","unstructured":"Ko\u010dvara, M., Stingl, M.: PENNON: a code for convex nonlinear and semidefinite programming. Optim. Methods Softw. 18, 317\u2013333 (2003)","journal-title":"Optim. Methods Softw."},{"key":"374_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-0265-0","volume-title":"Subdifferentials: Theory and Applications","author":"AG Kusraev","year":"1995","unstructured":"Kusraev, A.G., Kutateladze, S.S.: Subdifferentials: Theory and Applications. Kluwer Academic Publishers, Dordrecht (1995)"},{"key":"374_CR32","first-page":"1759","volume":"22","author":"GR Lanckriet","year":"2009","unstructured":"Lanckriet, G.R., Sriperumbudur, B.K.: On the convergence of the concave-convex procedure. Adv. Neural. Inf. Process. Syst. 22, 1759\u20131767 (2009)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"374_CR33","unstructured":"Leibfritz, F.: COMP$$l_e$$ib: COnstraint Matrix-optimization Problem library\u2014a collection of test examples for nonlinear semidefinite programs, control system design and related problems. Tech. rep., University of Trier, Department of Mathematics (2004). http:\/\/www.compleib.de"},{"key":"374_CR34","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s10479-004-5022-1","volume":"133","author":"HA Le Thi","year":"2005","unstructured":"Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23\u201346 (2005)","journal-title":"Ann. Oper. Res."},{"key":"374_CR35","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10107-018-1235-y","volume":"169","author":"HA Le Thi","year":"2018","unstructured":"Le Thi, H.A., Pham Dinh, T.: DC programming and DCA: thirty years of developments. Math. Program. 169, 5\u201368 (2018)","journal-title":"Math. Program."},{"key":"374_CR36","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/0167-6377(96)00022-3","volume":"19","author":"HA Le Thi","year":"1996","unstructured":"Le Thi, H.A., Pham Dinh, T., Muu, L.D.: Numerical solution for optimization over the efficient set by D.C. optimization algorithm. Oper. Res. Lett. 19, 117\u2013128 (1996)","journal-title":"Oper. Res. Lett."},{"key":"374_CR37","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1016\/S0377-2217(01)00301-0","volume":"142","author":"HA Le Thi","year":"2002","unstructured":"Le Thi, H.A., Pham Dinh, T., Thoai, N.V.: Combination between global and local methods for solving an optimization problem over the efficient set. Eur. J. Oper. Res. 142, 258\u2013270 (2002)","journal-title":"Eur. J. Oper. Res."},{"key":"374_CR38","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/978-3-319-06569-4_2","volume-title":"Advanced Computational Methods for Knowledge Engineering","author":"HA Le Thi","year":"2014","unstructured":"Le Thi, H.A., Nuynh, V.N., Pham Dinh, T.: DC programming and DCA for general DC programs. In: van Do, T., Thi, H.A.L., Nguyen, N.T. (eds.) Advanced Computational Methods for Knowledge Engineering, pp. 15\u201335. Springer, Berlin (2014)"},{"key":"374_CR39","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s10957-018-1345-y","volume":"179","author":"HA Le Thi","year":"2018","unstructured":"Le Thi, H.A., Nuynh, V.N., Pham Dinh, T.: Convergence analysis of difference-of-convex algorithm with subanalytic data. J. Optim. Theory Appl. 179, 103\u2013126 (2018)","journal-title":"J. Optim. Theory Appl."},{"key":"374_CR40","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/s11081-015-9294-x","volume":"17","author":"T Lipp","year":"2016","unstructured":"Lipp, T., Boyd, S.: Variations and extension of the convex-concave procedure. Optim. Eng. 17, 263\u2013287 (2016)","journal-title":"Optim. Eng."},{"key":"374_CR41","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1109\/78.984753","volume":"50","author":"JH Manton","year":"2002","unstructured":"Manton, J.H.: Optimization algorithms exploiting unitary constraints. IEEE Trans. Signal Process. 50, 635\u2013650 (2002)","journal-title":"IEEE Trans. Signal Process."},{"key":"374_CR42","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1287\/moor.2013.0622","volume":"39","author":"BS Mordukhovich","year":"2014","unstructured":"Mordukhovich, B.S., Nghia, T.: Nonsmooth cone-constrained optimization with applications to semi-infinite programming. Math. Oper. Res. 39, 301\u2013324 (2014)","journal-title":"Math. Oper. Res."},{"key":"374_CR43","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970791","volume-title":"Interior-Point Polynomial Algorithms in Convex Programming","author":"Y Nesterov","year":"1994","unstructured":"Nesterov, Y., Nemirovskii, A.: Interior-Point Polynomial Algorithms in Convex Programming. SIAM, Philadelphia (1994)"},{"key":"374_CR44","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/978-3-319-06569-4_3","volume-title":"Advanced Computational Methods for Knowledge Engineering","author":"YS Niu","year":"2014","unstructured":"Niu, Y.S., Dinh, T.P.: DC programming approaches for BMI and QMI feasibility problems. In: van Do, T., Thi, H., Nguyen, N. (eds.) Advanced Computational Methods for Knowledge Engineering, pp. 37\u201363. Springer, Cham (2014)"},{"key":"374_CR45","doi-asserted-by":"publisher","first-page":"403","DOI":"10.2140\/pjm.1983.107.403","volume":"107","author":"NS Papageorgiou","year":"1983","unstructured":"Papageorgiou, N.S.: Nonsmooth analysis on partially ordered vectors spaces: part 1\u2014convex case. Pac. J. Math. 107, 403\u2013458 (1983)","journal-title":"Pac. J. Math."},{"key":"374_CR46","first-page":"289","volume":"22","author":"T Pham Dinh","year":"1997","unstructured":"Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: theory, algorithms, and applications. Acta Math. Vietnamica 22, 289\u2013355 (1997)","journal-title":"Acta Math. Vietnamica"},{"key":"374_CR47","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1137\/S1052623494274313","volume":"8","author":"T Pham Dinh","year":"1998","unstructured":"Pham Dinh, T., Le Thi, H.A.: D.C. optimization algorithms for solving the trust region subproblem. SIAM J. Optim. 8, 476\u2013505 (1998)","journal-title":"SIAM J. Optim."},{"key":"374_CR48","first-page":"1","volume-title":"Transactions on Computational Intelligence XIII","author":"T Pham Dinh","year":"2014","unstructured":"Pham Dinh, T., Le Thi, H.A.: Recent advances in DC programming and DCA. In: Nguyen, N.T., Thi, H.A.L. (eds.) Transactions on Computational Intelligence XIII, pp. 1\u201337. Springer, Berlin (2014)"},{"key":"374_CR49","series-title":"North-Holland Mathematics Studies","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/S0304-0208(08)72402-2","volume-title":"Fermat Days 85: Mathematics for Optimization","author":"T Pham Dinh","year":"1986","unstructured":"Pham Dinh, T., Souad, E.B.: Algorithms for solving a class of nonconvex optimization problems. Methods of subgradients. In: Hiriart-Urruty, J.B. (ed.) Fermat Days 85: Mathematics for Optimization. North-Holland Mathematics Studies, vol. 129, pp. 249\u2013271. Norht-Holland, Amsterdam (1986)"},{"key":"374_CR50","doi-asserted-by":"crossref","unstructured":"Reemtsen, R., R\u00fcckmann, J.J. (eds.): Semi-Infinite Programming. Kluwer Academic Publishers, Dordrecht (1998)","DOI":"10.1007\/978-1-4757-2868-2"},{"key":"374_CR51","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1287\/moor.1.2.130","volume":"1","author":"SM Robinson","year":"1976","unstructured":"Robinson, S.M.: Regularity and stability for convex multivalued functions. Math. Oper. Res. 1, 130\u2013143 (1976)","journal-title":"Math. Oper. Res."},{"key":"374_CR52","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":"374_CR53","unstructured":"Stingl, M.: On the solution of nonlinear semidefinite programs by augmented Lagrangian methods. Ph.D. thesis, Institute of Applied Mathematics II, Friedrech-Alexander University of Erlangen-Nuremberg, Erlangen, Germany (2006)"},{"key":"374_CR54","first-page":"194","volume":"35","author":"AS Strekalovsky","year":"1987","unstructured":"Strekalovsky, A.S.: On the problem of the global extremum. Sov. Math. Dokl. 35, 194\u2013198 (1987)","journal-title":"Sov. Math. Dokl."},{"key":"374_CR55","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1023\/A:1008277314050","volume":"12","author":"AS Strekalovsky","year":"1998","unstructured":"Strekalovsky, A.S.: Global optimality conditions for nonconvex optimization. J. Glob. Optim. 12, 415\u2013434 (1998)","journal-title":"J. Glob. Optim."},{"key":"374_CR56","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/978-3-030-34910-3_7","volume-title":"Numerical Nonsmooth Optimization. State of the Art Algorithms","author":"AS Strekalovsky","year":"2020","unstructured":"Strekalovsky, A.S.: Local search for nonsmooth DC optimization with DC equality and inequality constraints. In: Bagirov, A.M., Gaudioso, M., Karmitsa, N., M\u00e4kel\u00e4, M.M., Taheri, S. (eds.) Numerical Nonsmooth Optimization. State of the Art Algorithms, pp. 229\u2013262. Springer, Cham (2020)"},{"key":"374_CR57","series-title":"Communications in Computer and Information Science","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1007\/978-3-030-38603-0_17","volume-title":"Optimization and Applications. OPTIMA 2019","author":"AS Strekalovsky","year":"2020","unstructured":"Strekalovsky, A.S.: On a global search in D.C. optimization problems. In: Ja\u0107imovi\u0107, M., Khachay, M., Malkova, V., Posypkin, M. (eds.) Optimization and Applications. OPTIMA 2019. Communications in Computer and Information Science, pp. 222\u2013236. Springer, Cham (2020)"},{"key":"374_CR58","first-page":"175","volume":"3","author":"AS Strekalovsky","year":"2021","unstructured":"Strekalovsky, A.S.: On global optimality conditions for D.C. minimization problems with D.C. constraints. J. Appl. Numer. Optim. 3, 175\u2013196 (2021)","journal-title":"J. Appl. Numer. Optim."},{"key":"374_CR59","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/0022-247X(81)90093-7","volume":"80","author":"M Thera","year":"1981","unstructured":"Thera, M.: Subdifferential calculus for convex operators. J. Math. Anal. Appl. 80, 78\u201391 (1981)","journal-title":"J. Math. Anal. Appl."},{"key":"374_CR60","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1017\/S0962492901000071","volume":"10","author":"M Todd","year":"2001","unstructured":"Todd, M.: Semidefinite optimization. Acta Numer. 10, 515\u2013560 (2001)","journal-title":"Acta Numer."},{"key":"374_CR61","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1016\/j.cam.2013.08.010","volume":"259","author":"AH Tor","year":"2014","unstructured":"Tor, A.H., Bagirov, A., Karas\u00f6zen, B.: Aggregate codifferential method for nonsmooth DC optimization. J. Comput. Appl. Math. 259, 851\u2013867 (2014)","journal-title":"J. Comput. Appl. Math."},{"key":"374_CR62","first-page":"63","volume":"1","author":"LT Tung","year":"2019","unstructured":"Tung, L.T.: Karush\u2013Kuhn\u2013Tucker optimality conditions for nonsmooth multiobjective semidefinite and semi-infinite programming. J. Appl. Numer. Optim. 1, 63\u201375 (2019)","journal-title":"J. Appl. Numer. Optim."},{"key":"374_CR63","series-title":"North-Holland Mathematics Studies","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/S0304-0208(08)72403-4","volume-title":"Fermat Days 85: Mathematics for Optimization","author":"H Tuy","year":"1986","unstructured":"Tuy, H.: A general deterministic approach to global optimization via D.C. programming. In: Hiriart-Urruty, J.B. (ed.) Fermat Days 85: Mathematics for Optimization. North-Holland Mathematics Studies, vol. 129, pp. 273\u2013303. Norht-Holland, Amsterdam (1986)"},{"key":"374_CR64","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2809-5","volume-title":"Convex Analysis and Global Optimization","author":"H Tuy","year":"1998","unstructured":"Tuy, H.: Convex Analysis and Global Optimization. Kluwer Academic Publishers, Dordrecht (1998)"},{"key":"374_CR65","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1023\/A:1024751811328","volume":"118","author":"H Tuy","year":"2003","unstructured":"Tuy, H.: On global optimality conditions and cutting plane algorithms. J. Optim. Theory Appl. 118, 201\u2013216 (2003)","journal-title":"J. Optim. Theory Appl."},{"key":"374_CR66","doi-asserted-by":"publisher","first-page":"890","DOI":"10.1080\/10556788.2019.1595619","volume":"34","author":"W van Ackooij","year":"2019","unstructured":"van Ackooij, W., de Oliveira, W.: Non-smooth DC-constrained optimization: constraint qualification and minimizing methodologies. Optim. Methods Softw. 34, 890\u2013920 (2019)","journal-title":"Optim. Methods Softw."},{"key":"374_CR67","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/s10957-019-01500-3","volume":"182","author":"W van Ackooij","year":"2019","unstructured":"van Ackooij, W., de Oliveira, W.: Nonsmooth and nonconvex optimization via approximate difference-of-convex decompositions. J. Optim. Theory Appl. 182, 49\u201380 (2019)","journal-title":"J. Optim. Theory Appl."},{"key":"374_CR68","unstructured":"van Ackooij, W., de\u00a0Oliveira, W.: Addendum to the paper \u201cNonsmooth DC-constrained optimization: constraint qualifications and minimizing methodologies\u201d (2020). https:\/\/www.researchgate.net\/publication\/348182693_Addendum_IDCA.pdf"},{"key":"374_CR69","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s10589-020-00241-8","volume":"78","author":"W van Ackooij","year":"2021","unstructured":"van Ackooij, W., Demassey, S., Javal, P., Morais, H., de Oliveira, W., Swaminathan, B.: A bundle method for nonsmooth dc programming with application to chance-constrained problems. Comput. Optim. Appl. 78, 451\u2013490 (2021)","journal-title":"Comput. Optim. Appl."},{"key":"374_CR70","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1080\/10556780902752447","volume":"24","author":"H Yamashita","year":"2009","unstructured":"Yamashita, H., Yabe, H.: A primal-dual interior point method for nonlinear optimization over second-order cones. Optim. Methods Softw. 24, 407\u2013426 (2009)","journal-title":"Optim. Methods Softw."},{"key":"374_CR71","first-page":"24","volume":"58","author":"H Yamashita","year":"2015","unstructured":"Yamashita, H., Yabe, H.: A survey of numerical methods for nonlinear semidefinite programming. J. Oper. Res. Soc. Jpn. 58, 24\u201360 (2015)","journal-title":"J. Oper. Res. Soc. Jpn."},{"key":"374_CR72","doi-asserted-by":"publisher","first-page":"915","DOI":"10.1162\/08997660360581958","volume":"15","author":"AL Yuille","year":"2003","unstructured":"Yuille, A.L., Rangarajan, A.: The concave-convex procedure. Neural Comput. 15, 915\u2013936 (2003)","journal-title":"Neural Comput."},{"key":"374_CR73","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s10898-012-9908-1","volume":"55","author":"Q Zhang","year":"2013","unstructured":"Zhang, Q.: A new necessary and sufficient global optimality condition for canonical DC problems. J. Glob. Optim. 55, 559\u2013577 (2013)","journal-title":"J. Glob. Optim."},{"key":"374_CR74","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1287\/moor.1060.0234","volume":"32","author":"XY Zheng","year":"2007","unstructured":"Zheng, X.Y., Yang, X.: Lagrange multipliers in nonsmooth semi-infinite optimization problems. Math. Oper. Res. 32, 168\u2013181 (2007)","journal-title":"Math. Oper. Res."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-022-00374-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-022-00374-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-022-00374-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T12:11:50Z","timestamp":1655727110000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-022-00374-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,4]]},"references-count":74,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["374"],"URL":"https:\/\/doi.org\/10.1007\/s10589-022-00374-y","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2022,5,4]]},"assertion":[{"value":"2 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 April 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}