Romano, G. New results in subdifferential calculus with applications to convex optimization. (English) Zbl 0828.49015 Appl. Math. Optimization 32, No. 3, 213-234 (1995). Summary: Chain and addition rules of subdifferential calculus are revisited in the paper and new proofs, providing local necessary and sufficient conditions for their validity, are presented. A new product rule pertaining to the composition of a convex functional and a Young function is also established and applied to obtain a proof of Kuhn-Tucker conditions in convex optimization under minimal assumptions on the data. Applications to plasticity theory are briefly outlined in the concluding remarks. Cited in 10 Documents MSC: 49J52 Nonsmooth analysis Keywords:optimization; subdifferential calculus; composition; convex functional; Young function; Kuhn-Tucker conditions; convex optimization; plasticity theory × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Clarke FH (1973) Necessary conditions for nonsmooth problems in optimal control and the calculus of variations. Thesis, University of Washington, Seattle, WA [2] Clarke FH (1983) Optimization and Nonsmooth Analysis. Wiley, New York · Zbl 0582.49001 [3] Ekeland I, Temam R (1974) Analyse convexe et problèmes variationnels. Dunod, Paris · Zbl 0281.49001 [4] Ioffe AD, Tihomirov VM (1979) The Theory of Extremal Problems. Nauka, Moscow (English translation, North-Holland, Amsterdam) [5] Laurent PJ (1972) Approximation et Optimisation. Hermann, Paris · Zbl 0238.90058 [6] McLinden L (1973) Dual operations on saddle functions. Trans Amer Math Soc 179:363-381 · Zbl 0275.90032 · doi:10.1090/S0002-9947-1973-0316097-1 [7] Moreau JJ (1966) Fonctionelles convexes. Lecture notes, séminaire: équationes aux dérivées partielles, Collège de France [8] Moreau JJ (1973) On unilateral constraints, friction and plasticity. New Variational Techniques in Mathematical Physics, CIME Bressanone, Ed. Cremonese, Roma, pp 171-322 [9] Panagiotopoulos PD (1985) Inequality Problems in Mechanics and Applications. Birkhäuser, Boston [10] Rockafellar RT (1963) Convex functions and dual extremum problems. Thesis Harvard, MA [11] Rockafellar RT (1970) Convex Analysis. Princeton University Press, Princeton, NJ · Zbl 0193.18401 [12] Rockafellar RT (1979) Directionally Lipschitzian functions and subdifferential calculus. Proc London Math Soc (3) 39:331-355 · Zbl 0413.49015 · doi:10.1112/plms/s3-39.2.331 [13] Rockafellar RT (1980) Generalized directional derivatives and subgradients of nonconvex functions. Canad J Math XXXII(2):257-280 · Zbl 0447.49009 · doi:10.4153/CJM-1980-020-7 [14] Rockafellar RT (1981) The Theory of Subgradients and its Applications to Problems of Optimization. Convex and Nonconvex Functions. Heldermann Verlag, Berlin · Zbl 0462.90052 [15] Romano G, Rosati L, Marotti de Sciarra F (1992) An internal variable theory of inelastic behaviour derived from the uniaxial rigid-perfectly plastic law. Internat J Engrg Sci 31(8):1105-1120 · Zbl 0781.73022 · doi:10.1016/0020-7225(93)90085-9 [16] Romano G, Rosati L, Marotti de Sciarra F (1993) Variational principles for a class of finite-step elasto-plastic problems with non-linear mixed hardening. Comput Methods Appl Mech Engrg 109:293-314 · Zbl 0845.73024 · doi:10.1016/0045-7825(93)90083-A [17] Romano G, Rosati L, Marotti de Sciarra F (1993) A variational theory for finite-step elasto-plastic problems. Internat J Solids 30(17):2317-2334 · Zbl 0781.73081 · doi:10.1016/0020-7683(93)90120-V [18] Slater M (1950) Lagrange multipliers revisited: a contribution to non-linear programming. Cowles Commission Discussion Paper, Math 403 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.