(TAYLOR & FRANCIS LTD, 2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND, 2019) Tor, Ali Hakan; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Tor, Ali Hakan
In this study, *-directional derivative and *-subgradient are defined using the multiplicative derivative, making a new contribution to non-Newtonian calculus for use in non-smooth analysis. As for directional derivative and subgradient, which are used in the non-smooth optimization theory, basic definitions and preliminary facts related to optimization theory are stated and proved, and the *-subgradient concept is illustrated by providing some examples, such as absolute value and exponential functions. In addition, necessary and sufficient optimality conditions are obtained for convex problems.