{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T21:50:21Z","timestamp":1770501021900,"version":"3.49.0"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[1992,8,1]],"date-time":"1992-08-01T00:00:00Z","timestamp":712627200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Programming"],"published-print":{"date-parts":[[1992,8]]},"DOI":"10.1007\/bf01580900","type":"journal-article","created":{"date-parts":[[2005,4,28]],"date-time":"2005-04-28T04:58:11Z","timestamp":1114664291000},"page":"223-232","source":"Crossref","is-referenced-by-count":16,"title":["Generalized convexity on affine subspaces with an application to potential functions"],"prefix":"10.1007","volume":"56","author":[{"given":"Jean-Pierre","family":"Crouzeix","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jacques A.","family":"Ferland","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siegfried","family":"Schaible","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"779","DOI":"10.2307\/1911819","volume":"29","author":"K.J. Arrow","year":"1961","unstructured":"K.J. Arrow and A.C. Enthoven, \u201cQuasi-concave programming,\u201dEconometrica 29 (1961) 779\u2013800.","journal-title":"Econometrica"},{"key":"CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-7600-2","volume-title":"Generalized Concavity","author":"M. Avriel","year":"1988","unstructured":"M. Avriel, W.E. Diewert, S. Schaible and I. Zang,Generalized Concavity (Plenum Press, New York and London, 1988)."},{"key":"CR3","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1007\/BF01588964","volume":"14","author":"M. Avriel","year":"1978","unstructured":"M. Avriel and S. Schaible, \u201cSecond order characterization of pseudo-convex functions,\u201dMathematical Programming 14 (1978) 170\u2013185.","journal-title":"Mathematical Programming"},{"key":"CR4","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/0024-3795(84)90150-2","volume":"63","author":"Y. Chabrillac","year":"1984","unstructured":"Y. Chabrillac and J.P. Crouzeix, \u201cDefiniteness and semidefiniteness of quadratic forms revisited,\u201dLinear Algebra and its Applications 63 (1984) 283\u2013292.","journal-title":"Linear Algebra and its Applications"},{"key":"CR5","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0024-3795(74)90066-4","volume":"8","author":"R.W. Cottle","year":"1974","unstructured":"R.W. Cottle, \u201cManifestations of the Schur Complement,\u201dLinear Algebra and its Applications 8 (1974) 189\u2013211.","journal-title":"Linear Algebra and its Applications"},{"key":"CR6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0024-3795(72)90022-5","volume":"5","author":"R.W. Cottle","year":"1972","unstructured":"R.W. Cottle and J.A. Ferland, \u201cMatrix-theoretic criteria for the quasi-convexity and pseudoconvexity of quadratic functions,\u201dLinear Algebra and its Applications 5 (1972) 123\u2013136.","journal-title":"Linear Algebra and its Applications"},{"key":"CR7","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF01588330","volume":"18","author":"J.P. Crouzeix","year":"1980","unstructured":"J.P. Crouzeix, \u201cA second order condition for quasi-convexity,\u201dMathematical Programming 18 (1980) 349\u2013352.","journal-title":"Mathematical Programming"},{"key":"CR8","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01583788","volume":"23","author":"J.P. Crouzeix","year":"1982","unstructured":"J.P. Crouzeix and J.A. Ferland, \u201cCriteria for quasi-convexity and pseudo-convexity: relationships and comparisons,\u201dMathematical Programming 23 (1982) 193\u2013205.","journal-title":"Mathematical Programming"},{"key":"CR9","doi-asserted-by":"crossref","first-page":"295","DOI":"10.2307\/1907852","volume":"20","author":"G. Debreu","year":"1952","unstructured":"G. Debreu, \u201cDefinite and Semidefinite quadratic forms,\u201dEconometrica 20 (1952) 295\u2013300.","journal-title":"Econometrica"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/0022-0531(81)90039-9","volume":"25","author":"W.E. Diewert","year":"1981","unstructured":"W.E. Diewert, M. Avriel and I. Zang: \u201cNine kinds of quasiconcavity and concavity,\u201dJournal of Economic Theory 25 (1981) 397\u2013420.","journal-title":"Journal of Economic Theory"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1007\/BF01585002","volume":"3","author":"J.A. Ferland","year":"1972","unstructured":"J.A. Ferland, \u201cMathematical programming problems with quasi-convex objective functions,\u201dMathematical Programming 3 (1972) 296\u2013301.","journal-title":"Mathematical Programming"},{"key":"CR12","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0024-3795(81)90007-0","volume":"38","author":"J.A. Ferland","year":"1981","unstructured":"J.A. Ferland, \u201cMatrix-theoretic criteria for the quasi-convexity of twice continuously differentiable functions,\u201dLinear Algebra and its Applications 38 (1981) 51\u201363.","journal-title":"Linear Algebra and its Applications"},{"key":"CR13","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF01580721","volume":"40","author":"H. Imai","year":"1988","unstructured":"H. Imai, \u201cOn the convexity of the multiplicative version of Karmarkar's potential function,\u201dMathematical Programming 40 (1988) 29\u201332.","journal-title":"Mathematical Programming"},{"key":"CR14","unstructured":"M. Iri and H. Imai, \u201cA multiplicative penalty function method for linear programming. Another \u201cnew and fast\u201d algorithm,\u201d in:Proceedings of the 6th Mathematical Programming Symposium of Japan (Tokyo, 1985) pp. 97\u2013120."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/BF01840457","volume":"1","author":"M. Iri","year":"1986","unstructured":"M. Iri and H. Imai, \u201cA multiplicative barrier function method for linear programming,\u201dAlgorithmica 1 (1986) 455\u2013482.","journal-title":"Algorithmica"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/BF02579150","volume":"4","author":"N. Karmarkar","year":"1984","unstructured":"N. Karmarkar, \u201cA new polynomial-type algorithm for linear programming,\u201dCombinatorica 4 (1984) 373\u2013395.","journal-title":"Combinatorica"},{"key":"CR17","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1137\/0127011","volume":"27","author":"P. Mereau","year":"1974","unstructured":"P. Mereau and J.G. Paquet, \u201cSecond order conditions for pseudo-convex functions,\u201dSIAM Journal on Applied Mathematics 27 (1974) 131\u2013137.","journal-title":"SIAM Journal on Applied Mathematics"},{"key":"CR18","first-page":"205","volume":"16","author":"S. Schaible","year":"1972","unstructured":"S. Schaible, \u201cQuasi-convex optimization in general real linear spaces,\u201dZeitschrift f\u00fcr Operations Research 16 (1972) 205\u2013213.","journal-title":"Zeitschrift f\u00fcr Operations Research"},{"key":"CR19","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/BF01581649","volume":"19","author":"S. Schaible","year":"1980","unstructured":"S. Schaible and I. Zang, \u201cOn the convexifiability of pseudoconvexC 2-functions,\u201dMathematical Programming 19 (1980) 289\u2013299.","journal-title":"Mathematical Programming"},{"key":"CR20","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/BF01840455","volume":"1","author":"M.J. Todd","year":"1986","unstructured":"M.J. Todd and B.P. Burrell, \u201cAn extension of Karmarkar's algorithm for linear programming using dual variables,\u201dAlgorithmica 1 (1986) 409\u2013424.","journal-title":"Algorithmica"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580900.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01580900\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01580900","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T11:12:12Z","timestamp":1556881932000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01580900"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,8]]},"references-count":20,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1992,8]]}},"alternative-id":["BF01580900"],"URL":"https:\/\/doi.org\/10.1007\/bf01580900","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,8]]}}}