Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Uwagi o zstępującym algorytmie numerycznym dla optymalizacji wypukłej funkcji nieróżniczkowalnych
Języki publikacji
Abstrakty
Albeit not often, nondifferentiable cost functions are encountered in some optimization problems, and are receiving considerable attention recently. For convex functions two generalizations of the notion of gradient have been devised, specifically subgradient, and ε-subgradient. These generalizations formed the basis for the development of generalized necessary and sufficient conditions for optimality, as well as the basis for numerical algorithms. Such algorithms require considerable computation necessary to find the direction of descent. Besides, they involve nonlinear programming technics. However, for nondifferentiable convex functions it is possible to "forget" about their nondifferentiability, i.e. to solve optimization problems involving such functions with classical algorithms devised for differentiable functions. (fragment of text)
Podano, przy pewnych dodatkowych założeniach, wariant metody D.P. Bertsekas'a i S.K. Mittera bardzo prosty w zastosowaniach. (abstrakt oryginalny)
Rocznik
Strony
62--65
Opis fizyczny
Twórcy
autor
- Academy of Agriculture in Poznań, Poland
Bibliografia
- Bertsekas D.P., S.K. Mitter, A descent numerical method for optimization problems with nondifferentiable cost functionals, SIAM J. Control 11 (1973), 639-652.
- Joffe A.D., W.M. Tichomirow, Theory of extremal problems (in Russian), Moskow 1974.
- Krasnosielskij M.A., J.B, Rutickij, Convex functions and Orlicz Spaces, Groningen 1961.
- Rockafellar R.T., Convex Analysis, Princeton University Press, Princeton, N.J. 1970.
- Sikorski R., Real functions (in Polish), Warsaw 1968.
- Stoer J., Ch. Witzgall, Convexity and Optimization in Finite Dimensions, Springer-Verlag Berlin, Heidelberg 1970.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171448850