{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T21:14:25Z","timestamp":1778966065564,"version":"3.51.4"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,3,21]],"date-time":"2017-03-21T00:00:00Z","timestamp":1490054400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2018,4]]},"DOI":"10.1007\/s11424-017-6085-9","type":"journal-article","created":{"date-parts":[[2017,3,21]],"date-time":"2017-03-21T01:17:13Z","timestamp":1490059033000},"page":"446-462","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Saddle Point Criteria in Nonsmooth Semi-Infinite Minimax Fractional Programming Problems"],"prefix":"10.1007","volume":"31","author":[{"given":"S. K.","family":"Mishra","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yadvendra","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. U.","family":"Verma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,3,21]]},"reference":[{"issue":"2","key":"6085_CR1","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1016\/S0377-2217(03)00266-2","volume":"153","author":"A Vaz","year":"2004","unstructured":"Vaz A, Ismael F, Fernandes Edite M G P, and Gomes M, Paula S F, Robot trajectory planning with semi-infinite programming, EURO young scientists-papers from the EURO Peripatetic Post-Graduate Programme (Paris,2001), European J. Oper. Res., 2004, 153(2): 607\u2013617.","journal-title":"European J. Oper. Res."},{"issue":"2","key":"6085_CR2","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1016\/j.cam.2007.02.026","volume":"217","author":"X Tong","year":"2008","unstructured":"Tong X, Ling C, and Qi L, A semi-infinite programming algorithm for solving optimal power flow with transient stability constraints, J. Comput. Appl. Math., 2008, 217(2): 432\u2013447.","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"6085_CR3","doi-asserted-by":"publisher","first-page":"1957","DOI":"10.1016\/j.apm.2008.05.008","volume":"33","author":"A Vaz","year":"2009","unstructured":"Vaz A, Ismael F, and Ferreira Eugnio C, Air pollution control with semi-infinite programming, Appl. Math. Model., 2009, 33(4): 1957\u20131969.","journal-title":"Appl. Math. Model."},{"issue":"3","key":"6085_CR4","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1016\/j.ejor.2007.01.057","volume":"191","author":"A Winterfeld","year":"2008","unstructured":"Winterfeld A, Application of general semi-infinite programming to lapidary cutting problems, European J. Oper. Res., 2008, 191(3): 838\u2013854.","journal-title":"European J. Oper. Res."},{"key":"6085_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-08114-4","volume-title":"Introduction to Nonsmooth Optimization: Theory, Practice and Software","author":"A Bagirov","year":"2014","unstructured":"Bagirov A, Karmitsa N, and M\u00e4kel\u00e4 M M, Introduction to Nonsmooth Optimization: Theory, Practice and Software, Springer, Heidelberg, New York, Dordrecht, London, 2014."},{"issue":"1","key":"6085_CR6","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.jmaa.2008.10.009","volume":"351","author":"N Kanzi","year":"2009","unstructured":"Kanzi N and Nobakhtian S, Nonsmooth semi-infinite programming problems with mixed constraints, J. Math. Anal. Appl., 2009, 351(1): 170\u2013181.","journal-title":"J. Math. Anal. Appl."},{"issue":"4","key":"6085_CR7","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1080\/01630563.2012.662199","volume":"33","author":"G J Zalmai","year":"2012","unstructured":"Zalmai G J and Zhang Q H, Optimality conditions and duality in nonsmooth semi infinite programming, Numer. Funct. Anal. Optim., 2012, 33(4): 452\u2013472.","journal-title":"Numer. Funct. Anal. Optim."},{"key":"6085_CR8","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/BF02191762","volume":"83","author":"Z F Li","year":"1984","unstructured":"Li Z F and Wang S Y, Lagrange multipliers and saddle points in multiobjective programming, J. Optim. Theory Appl., 1984, 83: 63\u201381.","journal-title":"J. Optim. Theory Appl."},{"key":"6085_CR9","first-page":"10","volume-title":"PA","author":"O L Mangasarian","year":"1994","unstructured":"Mangasarian O L, Nonlinear programming, corrected reprint of the 1969 original, Classics Appl. Math., Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994, 10."},{"key":"6085_CR10","volume-title":"Theory of Multiobjective Optimization","author":"Y Sawaragi","year":"1985","unstructured":"Sawaragi Y, Nakayama H, and Tanino T, Theory of Multiobjective Optimization, Academic Press. Inc. Orlando, 1985."},{"key":"6085_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-8395-6","volume-title":"Multiple-Criteria Decision Making: Concepts, Techniques and Extensions","author":"P L Yu","year":"1985","unstructured":"Yu P L, Multiple-Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York, 1985."},{"issue":"1","key":"6085_CR12","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/BF00939335","volume":"57","author":"Z K Xu","year":"1988","unstructured":"Xu Z K, Saddle-point type optimality criteria for generalized fractional programming, J. Optim. Theory Appl., 1988, 57(1): 189\u2013196.","journal-title":"J. Optim. Theory Appl."},{"key":"6085_CR13","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/BF02591906","volume":"27","author":"M A Lopez","year":"1983","unstructured":"Lopez M A and Vercher E, Optimality conditions for nondifferentiable convex semiinfinite programming, Math. Program., 1983, 27: 307\u2013319.","journal-title":"Math. Program."},{"key":"6085_CR14","first-page":"1","volume":"36","author":"T Antczak","year":"1983","unstructured":"Antczak T, Parametric saddle point criteria in semi-infinite minimax fractional programming problems under (p,r)-invexity, Num. Func. Anal. Optim., 1983, 36: 1\u201328.","journal-title":"Num. Func. Anal. Optim."},{"key":"6085_CR15","volume-title":"Optimization and Nonsmooth Analysis","author":"F H Clarke","year":"1983","unstructured":"Clarke F H, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983."},{"key":"6085_CR16","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1017\/S0004972700028604","volume":"42","author":"T W Reiland","year":"1990","unstructured":"Reiland T W, Nonsmooth invexity, Bull. Aust. Math. Soc., 1990, 42: 437\u2013446.","journal-title":"Bull. Aust. Math. Soc."},{"key":"6085_CR17","volume-title":"Linear Semi-Infinite Optimazation","author":"M A Goberna","year":"1987","unstructured":"Goberna M A and Lopez M A, Linear Semi-Infinite Optimazation, Wiley, Chichester, 1987."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-017-6085-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-017-6085-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-017-6085-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,5,29]],"date-time":"2018-05-29T09:10:58Z","timestamp":1527585058000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-017-6085-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,21]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["6085"],"URL":"https:\/\/doi.org\/10.1007\/s11424-017-6085-9","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,21]]}}}