Tor, Ali Hakan2020-02-032020-02-0320191658-365510.1080/16583655.2019.1580122https://hdl.handle.net/20.500.12573/101In 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.enginfo:eu-repo/semantics/openAccessOptimality conditionsnon-smooth convex analysismultiplicative calculusconvex analysisarticle10.1080/16583655.2019.1580122