An introduction to non-smooth convex analysis via multiplicative derivative

Tor A. H.

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, vol.13, no.1, pp.351-359, 2019 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1080/16583655.2019.1580122
  • Journal Name: JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.351-359
  • Keywords: Optimality conditions, non-smooth convex analysis, multiplicative calculus, convex analysis, OPTIMIZATION, MINIMIZATION, MODEL
  • Abdullah Gül University Affiliated: Yes

Abstract

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.