Decomposition in Terms of Variables for Some Optimization Problems
Decomposition of block convex-programming problems with coupling variables is considered in the paper. Functions of the blocks are defined on bounded sets. Rules for calculating ε-subgradients of objective functions of subproblems with connected variables are formulated. Initial problem normalization is described.
Unable to display preview. Download preview PDF.
- 1.Yu. P. Laptin and N. G. Zhurbenko, “Developing software for optimization of complex engineering objects,” in: Teor. Opt. Rishen' [in Ukrainian], Inst. kibern. im. V. M. Glushkova NAN Ukr. (2002), pp. 3-12.Google Scholar
- 2.N. Z. Shor, Nondifferentiable Optimization and Polynomial Problems, Kluwer Acad. Publ., London (1998).Google Scholar
- 3.C. Lemarechal, “An algorithm for minimizing convex functions,” in: Proc. IFIP Congr., North-Holland, Amsterdam (1974), pp. 552-556.Google Scholar
- 4.S. V. Rzhevskii, Monotone Methods of Convex Programming [in Russian], Naukova Dumka, Kiev (1993).Google Scholar
- 5.N. G. Zhurbenko, “On one ?-subgradients algorithm of minimization,” in: Teor. Opt. Rishen' [in Ukrainian], Inst. kibern. im. V. M. Glushkova NAN Ukr. (2002), pp. 111-118.Google Scholar
- 6.B. N. Pshenichnyi, The Linearization Method [in Russian], Nauka, Moscow (1983).Google Scholar
- 7.V. F. Dem'yanov and L. V. Vasil'ev, Nondifferentiable Optimization [in Russian], Nauka, Moscow (1981).Google Scholar
- 8.J. Condzio and J.-P. Vial, “Warm start and ?-subgradients in a cutting plane scheme for block-angular linear programs,” Comput. Optimiz. Appl., 14, 17-36 (1999).Google Scholar
- 9.D. B. Yudin and E. G. Gol'shtein, Linear Programming. Theory, Methods, and Applications [in Russian], Nauka, Moscow (1969).Google Scholar