Geodesic
Duality and calculus of convex objects (theory and
Sbornik. Mathematics, Tome 198 (2007) no. 2, pp. 171-206 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme ‘Duality formulae and the calculus of convex objects’ is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles. 
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J. Brinkhuis; V. M. Tikhomirov. Duality and calculus of convex objects (theory and. Sbornik. Mathematics, Tome 198 (2007) no. 2, pp. 171-206. http://geodesic.mathdoc.fr/item/SM_2007_198_2_a1/

[1] G. G. Magaril-Ilyaev, V. M. Tikhomirov, Vypuklyi analiz i ego prilozheniya, URSS, M., 2003

[2] J. Brinkhuis, V. Tikhomirov, Optimization: insights and applications, Princeton Univ. Press, Princeton, NJ, 2005 | MR | Zbl

[3] H. Minkowski, Theorie der konvexe Körper, Gesammelte Abhandlungen, 2, Teubner, Leipzig, 1910

[4] W. Fenchel, “On conjugate convex functions”, Canad. J. Math., 1 (1949), 73–77 | MR | Zbl

[5] R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, NJ, 1970 ; R. Rokafellar, Vypuklyi analiz, Mir, M., 1973 | MR | Zbl