{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,9]],"date-time":"2025-11-09T07:31:26Z","timestamp":1762673486244},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2005,7,14]],"date-time":"2005-07-14T00:00:00Z","timestamp":1121299200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2005,11]]},"DOI":"10.1007\/s10107-005-0614-3","type":"journal-article","created":{"date-parts":[[2005,7,14]],"date-time":"2005-07-14T12:41:47Z","timestamp":1121344907000},"page":"229-233","source":"Crossref","is-referenced-by-count":51,"title":["A new geometric condition for Fenchel's duality in infinite dimensional spaces"],"prefix":"10.1007","volume":"104","author":[{"given":"Regina Sandra","family":"Burachik","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vaithilingam","family":"Jeyakumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,7,14]]},"reference":[{"key":"614_CR1","doi-asserted-by":"crossref","unstructured":"Attouch, H., Br\u00e9zis, H.: Duality for the sum of convex functions in general Banach spaces. In: J.A. Barroso (ed) Aspects of Mathematics and its applications, North Holland, Amsterdam, pp 125\u2013133, 1986","DOI":"10.1016\/S0924-6509(09)70252-1"},{"key":"614_CR2","first-page":"1","volume":"34","author":"Br\u00f8ndsted","year":"1964","unstructured":"Br\u00f8ndsted, A.: Conjugate convex functions in topological vector spaces. Fys. Medd. Dans. Vid. Selsk. 34, 1\u201326 (1964)","journal-title":"Fys. Medd. Dans. Vid. Selsk."},{"key":"614_CR3","unstructured":"Ekeland, I., Temam, R.: Convex analysis and variational problems. North Holland, Amsterdam, 1976"},{"key":"614_CR4","unstructured":"Fenchel, W.: Convex cones, sets and functions. Lecture Notes, Princeton University, Princeton, 1953"},{"key":"614_CR5","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1137\/0328051","volume":"28","author":"Gowda","year":"4","unstructured":"Gowda, M.S., Teboulle, M.: A comparison of constraint qualifications in infinite-dimensional convex programming. SIAM J. Control and Optim. 28 (4), 925\u2013935 (1990)","journal-title":"SIAM J. Control and Optim."},{"key":"614_CR6","unstructured":"Hiriart-Urruty, J.-B.: -subdifferential calculus. In: Convex Analysis and Optimization, Pitman, Boston, pp 43\u201392, 1982"},{"key":"614_CR7","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1006\/jfan.1993.1141","volume":"118","author":"Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.-B., Phelps, R.R.: Subdifferential Calculus using \u03b5-subdifferentials. J. of Funct. Anal. 118, 154\u2013166 (1993)","journal-title":"J. of Funct. Anal."},{"key":"614_CR8","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1016\/0362-546X(90)90047-K","volume":"15","author":"Jeyakumar","year":"1990","unstructured":"Jeyakumar, V.: Duality and infinite dimensional optimization. Nonlinear Anal 15, 1111\u20131122 (1990)","journal-title":"Nonlinear Anal"},{"key":"614_CR9","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1137\/S1052623402401944","volume":"13","author":"Jeyakumar","year":"2003","unstructured":"Jeyakumar, V.: Characterizing set containments involving infinite convex constraints and reverse-convex constraints. SIAM J. Optim. 13, 947\u2013959 (2003)","journal-title":"SIAM J. Optim."},{"key":"614_CR10","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1137\/S1052623402417699","volume":"14","author":"Jeyakumar","year":"2","unstructured":"Jeyakumar, V., Lee, G.M., Dinh, N.: New sequential Lagrange multiplier conditions characterizing optimality without constraint qualifications for convex programs. SIAM J. Optim. 14 (2), 534\u2013547 (2003)","journal-title":"SIAM J. Optim."},{"key":"614_CR11","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/BF01581074","volume":"57","author":"Jeyakumar","year":"1","unstructured":"Jeyakumar, V., Wolkowicz, H.: Generalizations of Slater \u2032s constraint qualification for infinite convex programs. Math. Progr. 57 (1), 85\u2013102 (1992)","journal-title":"Math. Progr."},{"key":"614_CR12","unstructured":"Moreau, J.-J.: Fonctionnelles convexes. Coll\u00e8ge de France, Lecture Notes, 1967"},{"key":"614_CR13","first-page":"109","volume":"49","author":"Moreau","year":"1970","unstructured":"Moreau, J.-J.: Inf-convolution, sous-additivit\u00e9, convexit\u00e9 des fonctions numeriques. Journal de Matematiques Pures et Appliqu\u00e9es 49, 109\u2013154 (1970)","journal-title":"Journal de Matematiques Pures et Appliqu\u00e9es"},{"key":"614_CR14","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1016\/j.na.2003.07.008","volume":"25","author":"Ng","year":"2003","unstructured":"Ng, K.F., Song, W.: Fenchel duality in infinite-dimensional setting and its applications. Nonlinear Analysis 25, 845\u2013858 (2003)","journal-title":"Nonlinear Analysis"},{"key":"614_CR15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/02331939008843516","volume":"21","author":"Rodrigues","year":"1990","unstructured":"Rodrigues, B.: The Fenchel duality Theorem in Fr\u00e9chet spaces. Optim 21, 13\u201322 (1990)","journal-title":"Optim"},{"key":"614_CR16","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1016\/0362-546X(90)90071-N","volume":"14","author":"Simons","year":"1990","unstructured":"Simons, S.: The occasional distributivity of o over +e and the change of variable formula for conjugate functions. Nonlinear Anal 14, 1111\u20131120 (1990)","journal-title":"Nonlinear Anal"},{"key":"614_CR17","first-page":"1","volume":"352","author":"Str\u00f6mberg","year":"1996","unstructured":"Str\u00f6mberg, T.: The operation of infimal convolution. Diss. Math. 352, 1\u201361 (1996)","journal-title":"Diss. Math."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-005-0614-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-005-0614-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-005-0614-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T05:49:58Z","timestamp":1559108998000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-005-0614-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,7,14]]},"references-count":17,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2005,11]]}},"alternative-id":["614"],"URL":"https:\/\/doi.org\/10.1007\/s10107-005-0614-3","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,7,14]]}}}