Tor, Ali Hakan2025-09-252025-09-2520191658-3655https://doi.org/10.1080/16583655.2019.1580122https://hdl.handle.net/20.500.12573/3262Tor, Ali Hakan/0000-0003-3193-5004;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.eninfo:eu-repo/semantics/openAccessOptimality ConditionsNon-Smooth Convex AnalysisMultiplicative CalculusConvex AnalysisArticle10.1080/16583655.2019.15801222-s2.0-85132090927