Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IM2_2009_73_1_a1, author = {M. Yu. Andramonov}, title = {Convergence of a numerical abstract convexity algorithm}, journal = {Izvestiya. Mathematics }, pages = {3--19}, publisher = {mathdoc}, volume = {73}, number = {1}, year = {2009}, language = {en}, url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_1_a1/} }
M. Yu. Andramonov. Convergence of a numerical abstract convexity algorithm. Izvestiya. Mathematics , Tome 73 (2009) no. 1, pp. 3-19. http://geodesic.mathdoc.fr/item/IM2_2009_73_1_a1/
[1] S. S. Kutateladze, A. M. Rubinov, Dvoistvennost Minkovskogo i ee prilozheniya, Nauka, Novosibirsk, 1976 | MR
[2] V. L. Levin, “Semiconical sets, semi-homogeneous functions, and a new duality scheme in convex analysis”, Russian Acad. Sci. Dokl. Math., 55:3 (1997), 421–423 | MR | Zbl
[3] A. Rubinov, Abstract convexity and global optimization, Nonconvex Optim. Appl., 44, Kluwer Acad. Publ., Dordrecht, 2000 | MR | Zbl
[4] D. Pallaschke, S. Rolewicz, Foundations of mathematical optimization. Convex analysis without linearity, Math. Appl., 388, Kluwer Acad. Publ., Dordrecht, 1997 | MR | Zbl
[5] I. Singer, Abstract convex analysis, Canad. Math. Soc. Ser. Monogr. Adv. Texts, Wiley, New York, 1997 | MR | Zbl
[6] A. M. Rubinov, B. M. Glover, V. Jeyakumar, “A general approach to dual characterizations of solvability of inequality systems with applications”, J. Convex Anal., 2:1–2 (1995), 309–344 | MR | Zbl
[7] A. M. Rubinov, B. M. Glover, “Increasing convex-along-rays functions with applications to global optimization”, J. Optim. Theory Appl., 102:3 (1999), 615–642 | DOI | MR | Zbl
[8] J. E. Kelley, jr., “The cutting-plane method for solving convex programs”, J. Soc. Indust. Appl. Math., 8:4 (1960), 703–712 | DOI | MR | Zbl
[9] M. Andramonov, A. Rubinov, B. Glover, “Cutting angle methods in global optimization”, Appl. Math. Lett., 12:3 (1999), 95–100 | DOI | MR | Zbl
[10] M. Yu. Andramonov, A. M. Rubinov, B. M. Glover, Cutting angle method for minimizing increasing convex-along-rays functions, Research Report, University of Ballarat, 1997
[11] E. Balas, “Disjunctive programming”, Discrete optimization II, Proc. Adv. Res. Inst. Discrete Optimization and Systems Appl. (Banff, 1977), Ann. Discrete Math., 5, 1979, 3–51 | DOI | MR | Zbl
[12] N. Beaumont, “An algorithm for disjunctive programs”, European J. Oper. Res., 48:3 (1990), 362–371 | DOI | Zbl
[13] R. Horst, H. Tuy, Global optimization. Deterministic approaches, Springer-Verlag, Berlin, 1990 | MR | Zbl
[14] J. D. Pintér, Global optimization in action. Continuous and Lipschitz optimization: algorithms, implementations and applications, Nonconvex Optim. Appl., 6, Kluwer Acad. Publ., Dordrecht, 1996 | MR | Zbl
[15] Handbook of global optimization, Nonconvex Optim. Appl., 2, eds. R. Horst, M. P. Pardalos, Kluwer Acad. Publ., Dordrecht, 1995 | MR | Zbl