{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T23:02:49Z","timestamp":1769727769278,"version":"3.49.0"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2014,9]]},"DOI":"10.1007\/s10957-013-0512-4","type":"journal-article","created":{"date-parts":[[2013,12,31]],"date-time":"2013-12-31T16:21:31Z","timestamp":1388506891000},"page":"718-734","source":"Crossref","is-referenced-by-count":23,"title":["Duality Theory and Applications to Unilateral Problems"],"prefix":"10.1007","volume":"162","author":[{"given":"Patrizia","family":"Daniele","sequence":"first","affiliation":[]},{"given":"Sofia","family":"Giuffr\u00e8","sequence":"additional","affiliation":[]},{"given":"Antonino","family":"Maugeri","sequence":"additional","affiliation":[]},{"given":"Fabio","family":"Raciti","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,1,1]]},"reference":[{"key":"512_CR1","series-title":"Conference board of the Mathematical Science regional Conference Series in Applied Mathematics","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970524","volume-title":"Conjugate Duality and Optimization","author":"R.T. Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Conjugate Duality and Optimization. Conference board of the Mathematical Science regional Conference Series in Applied Mathematics, vol. 16. Society for Industrial and Applied Mathematics, Philadelphia (1974)"},{"key":"512_CR2","volume-title":"Geometric Functional Analysis","author":"R.B. Holmes","year":"1975","unstructured":"Holmes, R.B.: Geometric Functional Analysis. Springer, Berlin (1975)"},{"key":"512_CR3","unstructured":"Borwein, J.M., Jeyakumar, V., Lewis, A.S., Wolkowicz, M.: Constrained approximation via convex programming. Preprint, University of Waterloo (1988)"},{"key":"512_CR4","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/BF01581074","volume":"57","author":"V. Jeyakumar","year":"1992","unstructured":"Jeyakumar, V., Wolkowicz, H.: Generalizations of slater constraint qualification for infinite convex programs. Math. Program. 57, 85\u2013101 (1992)","journal-title":"Math. Program."},{"key":"512_CR5","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1080\/02331930903578684","volume":"60","author":"A. Barbagallo","year":"2011","unstructured":"Barbagallo, A., Maugeri, A.: Duality theory for a dynamic oligopolistic market equilibrium problem. Optimization 60, 29\u201352 (2011)","journal-title":"Optimization"},{"key":"512_CR6","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1007\/s10957-005-7502-0","volume":"127","author":"M.G. Cojocaru","year":"2005","unstructured":"Cojocaru, M.G., Daniele, P., Nagurney, A.: Projected dynamical systems and evolutionary variational inequalities via Hilbert spaces and applications. J. Optim. Theory Appl. 127, 549\u2013563 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"512_CR7","doi-asserted-by":"crossref","DOI":"10.4337\/9781781008164","volume-title":"Dynamic Networks and Evolutionary Variational Inequalities","author":"P. Daniele","year":"2006","unstructured":"Daniele, P.: Dynamic Networks and Evolutionary Variational Inequalities. Edward Elgar, Cheltenham (2006)"},{"key":"512_CR8","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1016\/j.tre.2010.03.005","volume":"46","author":"P. Daniele","year":"2010","unstructured":"Daniele, P.: Evolutionary variational inequalities and applications to complex dynamic multi-level models. Transportation Research Part E 46, 855\u2013880 (2010)","journal-title":"Transportation Research Part E"},{"key":"512_CR9","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s11590-006-0028-z","volume":"1","author":"P. Daniele","year":"2007","unstructured":"Daniele, P., Giuffr\u00e9, S.: General infinite dimensional duality and applications to evolutionary network equilibrium problems. Optim. Lett. 1, 227\u2013243 (2007)","journal-title":"Optim. Lett."},{"key":"512_CR10","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s00208-007-0118-y","volume":"339","author":"P. Daniele","year":"2007","unstructured":"Daniele, P., Giuffr\u00e9, S., Idone, G., Maugeri, A.: Infinite dimensional duality and applications. Math. Ann. 339, 221\u2013239 (2007)","journal-title":"Math. Ann."},{"key":"512_CR11","first-page":"537","volume":"4","author":"M.B. Donato","year":"2008","unstructured":"Donato, M.B., Maugeri, A., Milasi, M., Vitanza, C.: Duality theory for a dynamic Walrasian pure exchange economy. Pac. J. Optim. 4, 537\u2013547 (2008)","journal-title":"Pac. J. Optim."},{"key":"512_CR12","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1016\/j.mcm.2005.12.007","volume":"43","author":"J. Gwinner","year":"2006","unstructured":"Gwinner, J., Raciti, F.: Random equilibrium problems on networks. Math. Comput. Model. 43, 880\u2013891 (2006)","journal-title":"Math. Comput. Model."},{"key":"512_CR13","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1080\/01630560600790819","volume":"27","author":"J. Gwinner","year":"2006","unstructured":"Gwinner, J., Raciti, F.: On a class of random variational inequalities on random sets. Numer. Funct. Anal. Optim. 27, 619\u2013636 (2006)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"512_CR14","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.11650\/twjm\/1500405610","volume":"13","author":"G. Idone","year":"2009","unstructured":"Idone, G., Maugeri, A.: Generalized constraints qualification and infinite dimensional duality. Taiwan. J. Math. 13, 1711\u20131722 (2009)","journal-title":"Taiwan. J. Math."},{"key":"512_CR15","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1007\/s10957-012-9995-7","volume":"154","author":"L. Scrimali","year":"2012","unstructured":"Scrimali, L.: Infinite dimensional duality theory applied to investment strategies in environmental policy. J. Optim. Theory Appl. 154, 258\u2013277 (2012)","journal-title":"J. Optim. Theory Appl."},{"key":"512_CR16","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/BF00281472","volume":"49","author":"H. Brezis","year":"1972","unstructured":"Brezis, H.: Moltiplicateur de Lagrange en torsion elasto-plastique. Arch. Ration. Mech. Anal. 49, 32\u201340 (1972)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"512_CR17","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10957-008-9412-4","volume":"139","author":"R.I. Bot","year":"2008","unstructured":"Bot, R.I., Csetnek, E.R., Moldovan, A.: Revisiting some dual theorems via the quasirelative interior in convex optimization. J. Optim. Theory Appl. 139, 67\u201384 (2008)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"512_CR18","first-page":"567","volume":"13","author":"P. Daniele","year":"2009","unstructured":"Daniele, P., Giuffr\u00e9, S., Maugeri, A.: Remarks on general infinite dimensional duality with cone and equality constraints. Commun. Appl. Anal. 13(4), 567\u2013578 (2009)","journal-title":"Commun. Appl. Anal."},{"key":"512_CR19","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.jmaa.2009.09.006","volume":"364","author":"A. Grad","year":"2010","unstructured":"Grad, A.: Quasi-relative interior-type constraints qualifications ensuring strong Lagrange duality for optimization problems with cone and affine constraints. J. Math. Anal. Appl. 364, 86\u201395 (2010)","journal-title":"J. Math. Anal. Appl."},{"key":"512_CR20","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s10898-009-9442-y","volume":"46","author":"A. Maugeri","year":"2010","unstructured":"Maugeri, A., Raciti, F.: Remarks on infinite dimensional duality. J. Glob. Optim. 46, 581\u2013588 (2010)","journal-title":"J. Glob. Optim."},{"key":"512_CR21","unstructured":"Zalinescu, C.: Private communications: September 4th, 5th, 7th, October 10th (2007)"},{"key":"512_CR22","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1007\/BF00250529","volume":"41","author":"H. Brezis","year":"1971","unstructured":"Brezis, H., Sibony, M.: Equivalence de Deux In\u00e9quation Variationnelles et Application. Arch. Ration. Mech. Anal. 41, 254\u2013265 (1971)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"512_CR23","first-page":"520","volume":"264","author":"H. Lanchon","year":"1967","unstructured":"Lanchon, H., Duvaut, G.: Sur la Solution du probleme de torsion \u00e9lastoplastic d\u2019une bare cylindrique de section quelconque. C. R. Acad. Sci. Paris, Ser. A 264, 520\u2013523 (1967)","journal-title":"C. R. Acad. Sci. Paris, Ser. A"},{"key":"512_CR24","first-page":"791","volume":"269","author":"H. Lanchon","year":"1969","unstructured":"Lanchon, H.: Solution du probleme de torsion \u00e9lastoplastic d\u2019une bare cylindrique de section quelconque. C. R. Acad. Sci. Paris, Ser. A 269, 791\u2013794 (1969)","journal-title":"C. R. Acad. Sci. Paris, Ser. A"},{"key":"512_CR25","volume-title":"Obstacle Problems in Mathematical Physics","author":"J.F. Rodriguez","year":"1987","unstructured":"Rodriguez, J.F.: Obstacle Problems in Mathematical Physics. North-Holland, Amsterdam (1987)"},{"issue":"1","key":"512_CR26","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1137\/07068432X","volume":"19","author":"R.I. Bot","year":"2008","unstructured":"Bot, R.I., Csetnek, E.R., Wanka, G.: Regularity conditions via quasi-relative interior in convex programming. SIAM J. Optim. 19(1), 217\u2013233 (2008)","journal-title":"SIAM J. Optim."},{"key":"512_CR27","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF01581072","volume":"57","author":"J.M. Borwein","year":"1992","unstructured":"Borwein, J.M., Lewis, A.S.: Partially finite convex programming, part I: quasi relative interiors and duality theory. Math. Program. 57, 15\u201348 (1992)","journal-title":"Math. Program."},{"key":"512_CR28","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1016\/S0895-7177(02)80030-9","volume":"35","author":"P. Daniele","year":"2002","unstructured":"Daniele, P., Maugeri, A.: Variational inequalities and discrete continuum models of network equilibrium. Probl. Math. Comput. Model. 35, 689\u2013708 (2002)","journal-title":"Probl. Math. Comput. Model."},{"issue":"1","key":"512_CR29","doi-asserted-by":"crossref","first-page":"39","DOI":"10.3934\/jimo.2005.1.39","volume":"1","author":"P. Daniele","year":"2005","unstructured":"Daniele, P., Giuffr\u00e9, S., Pia, S.: Competitive financial equilibrium problems with policy interventions. J. Ind. Manag. Optim. 1(1), 39\u201352 (2005)","journal-title":"J. Ind. Manag. Optim."},{"issue":"3","key":"512_CR30","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1142\/S0218202508002711","volume":"18","author":"M.B. Donato","year":"2008","unstructured":"Donato, M.B., Milasi, M., Vitanza, C.: Quasi-variational approach of a competitive economic equilibrium problem with utility function: existence of equilibrium. Math. Models Methods Appl. Sci. 18(3), 351\u2013367 (2008)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"512_CR31","unstructured":"Giannessi, F., Maugeri, A.: Preface of the special issue on the proceedings of the first AMS-UMI joint meeting. J. Glob. Optim. 28 (2004)"},{"key":"512_CR32","doi-asserted-by":"crossref","first-page":"81","DOI":"10.3934\/jimo.2005.1.81","volume":"1","author":"G. Idone","year":"2005","unstructured":"Idone, G., Maugeri, A.: Variational inequalities and transport planning for an elastic and continuous model. J. Ind. Manag. Optim. 1, 81\u201386 (2005)","journal-title":"J. Ind. Manag. Optim."},{"key":"512_CR33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10898-007-9272-8","volume":"40","author":"A. Maugeri","year":"2008","unstructured":"Maugeri, A., Murthy, M.K.V., Trudinger, N.: Preface of the variational analysis and partial differential equations. In memory of Sergio Campanato and Guido Stampacchia. J. Glob. Optim. 40, 1\u20135 (2008)","journal-title":"J. Glob. Optim."},{"key":"512_CR34","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s11590-007-0044-7","volume":"2","author":"A. Maugeri","year":"2008","unstructured":"Maugeri, A., Raciti, F.: On general infinite dimensional complementarity problems. Optim. Lett. 2, 71\u201390 (2008)","journal-title":"Optim. Lett."},{"key":"512_CR35","volume-title":"Theory of Perfectly Plastic Solids","author":"W. Prager","year":"1951","unstructured":"Prager, W., Hodge, P.G.: Theory of Perfectly Plastic Solids. Wiley, New York (1951)"},{"key":"512_CR36","first-page":"369","volume":"113","author":"T.W. Ting","year":"1966","unstructured":"Ting, T.W.: Elastic-plastic torsion of a square bar. Trans. Am. Math. Soc. 113, 369\u2013401 (1966)","journal-title":"Trans. Am. Math. Soc."},{"key":"512_CR37","first-page":"31","volume":"73","author":"R.S.R. Schultze","year":"2009","unstructured":"Schultze, R.S.R.: Von Mises (1883\u20131953): a pioneer of applied mathematics in four countries. Newsl.\u2014Eur. Math. Soc. 73, 31\u201334 (2009)","journal-title":"Newsl.\u2014Eur. Math. Soc."},{"key":"512_CR38","unstructured":"Von Mises, R.: Mechanik der festen K\u00f6rper im plastish deformablem Zustand. Nachr. Ges. Wiss. Goett., Math.-Phys. Kl. 582\u2013592, (1913)"},{"key":"512_CR39","series-title":"Reissner Anniversary Volume","volume-title":"Three Remarks on the Theory of the Ideal Plastic Body","author":"R. Mises Von","year":"1949","unstructured":"Von Mises, R.: Three Remarks on the Theory of the Ideal Plastic Body. Reissner Anniversary Volume. Edwards, Ann Arbor (1949)"},{"key":"512_CR40","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1007\/BF00291936","volume":"25","author":"T.W. Ting","year":"1967","unstructured":"Ting, T.W.: Elastic-plastic torsion problem II. Arch. Ration. Mech. Anal. 25, 342\u2013366 (1967)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"512_CR41","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/BF00281140","volume":"34","author":"T.W. Ting","year":"1969","unstructured":"Ting, T.W.: Elastic-plastic torsion problem III. Arch. Ration. Mech. Anal. 34, 228\u2013244 (1969)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"512_CR42","volume-title":"Variational Principles and Free Boundary Problems","author":"A. Friedman","year":"1982","unstructured":"Friedman, A.: Variational Principles and Free Boundary Problems. Wiley, New York (1982)"},{"key":"512_CR43","first-page":"1","volume":"51","author":"H. Brezis","year":"1972","unstructured":"Brezis, H.: Probl\u00e9mes Unilat\u00e9raux. J. Math. Pures Appl. 51, 1\u2013168 (1972)","journal-title":"J. Math. Pures Appl."},{"key":"512_CR44","first-page":"281","volume-title":"Symposia Mathematica","author":"G. Stampacchia","year":"1972","unstructured":"Stampacchia, G.: On a problem of numerical analysis connected with the theory of variational inequalities. In: Symposia Mathematica, vol. X, pp. 281\u2013293. Academic Press, San Diego (1972)"},{"key":"512_CR45","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1006\/jdeq.1994.1161","volume":"114","author":"V. Chiad\u00f3-Piat","year":"1994","unstructured":"Chiad\u00f3-Piat, V., Percivale, D.: Generalized Lagrange multipliers in elastoplastic torsion. J. Differ. Equ. 114, 570\u2013579 (1994)","journal-title":"J. Differ. Equ."},{"issue":"8","key":"512_CR46","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1016\/j.jfa.2011.06.006","volume":"261","author":"M.B. Donato","year":"2011","unstructured":"Donato, M.B.: The infinite dimensional Lagrange multiplier rule for convex optimization problems. J. Funct. Anal. 261(8), 2083\u20132093 (2011)","journal-title":"J. Funct. Anal."},{"key":"512_CR47","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.2298\/FIL1205029G","volume":"26","author":"S. Giuffr\u00e8","year":"2012","unstructured":"Giuffr\u00e8, S., Maugeri, A.: New results on infinite dimensional duality in elastic\u2013plastic torsion. Filomat 26, 1029\u20131036 (2012)","journal-title":"Filomat"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-013-0512-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-013-0512-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-013-0512-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,9]],"date-time":"2023-07-09T11:22:42Z","timestamp":1688901762000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-013-0512-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,1]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,9]]}},"alternative-id":["512"],"URL":"https:\/\/doi.org\/10.1007\/s10957-013-0512-4","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,1]]}}}