Some Remarks on a Descent Numerical Algorithm for Convex Optimization Problems Involving Nondifferentiable Functions

• Autorzy: Zbigniew Kabała

Warianty tytułu

Uwagi o zstępującym algorytmie numerycznym dla optymalizacji wypukłej funkcji nieróżniczkowalnych

• Języki publikacji: EN

Abstrakty

EN

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)

Słowa kluczowe

EN

Functions; Mathematical functions; Numeric algorithms

PL

Funkcje; Funkcje matematyczne; Algorytmy numeryczne

• Czasopismo: Zeszyty Naukowe. Seria 1 / Akademia Ekonomiczna w Poznaniu
• Rocznik: 1985
• Numer: nr 132 Papers on Numerical Methods and Their Applications
• Strony: 62--65

Twórcy

autor

Zbigniew Kabała

• 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.