Proper and adjoint exhausters in nonsmooth analysis: optimality conditions

M.E. Abbasov, V.F. Demyanov

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучная

15 Цитирования (Scopus)

Аннотация

The notions of upper and lower exhausters represent generalizations of the notions of exhaustive families of upper convex and lower concave approximations (u.c.a., l.c.a.). The notions of u.c.a.’s and l.c.a.’s were introduced by Pshenichnyi (Convex Analysis and Extremal Problems, Series in Nonlinear Analysis and its Applications, 1980), while the notions of exhaustive families of u.c.a.’s and l.c.a.’s were described by Demyanov and Rubinov in Nonsmooth Problems of Optimization Theory and Control, Leningrad University Press, Leningrad, 1982. These notions allow one to solve the problem of optimization of an arbitrary function by means of Convex Analysis thus essentially extending the area of application of Convex Analysis. In terms of exhausters it is possible to describe extremality conditions, and it turns out that conditions for a minimum are expressed via an upper exhauster while conditions for a maximum are formulated in terms of a lower exhauster (Abbasov and Demyanov (2010), Demyanov and Roshchina (Appl
Язык оригиналаанглийский
Название основной публикацииProper and adjoint exhausters in nonsmooth analysis: optimality conditions
ИздательSpringer Nature
Страницы569-585
ISBN (печатное издание)0925-5001
DOI
СостояниеОпубликовано - 2013

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