On global subdifferentials with applications in nonsmooth optimization

Felipe Lara () and Alireza Kabgani ()
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Felipe Lara: Universidad de Tarapacá
Alireza Kabgani: Urmia University of Technology

Journal of Global Optimization, 2021, vol. 81, issue 4, No 3, 900 pages

Abstract: Abstract The notions of global subdifferentials associated with the global directional derivatives are introduced in the following paper. Most common used properties, a set of calculus rules along with a mean value theorem are presented as well. In addition, a diversity of comparisons with well-known subdifferentials such as Fréchet, Dini, Clarke, Michel–Penot, and Mordukhovich subdifferential and convexificator notion are provided. Furthermore, the lower global subdifferential is in fact proved to be an abstract subdifferential. Therefore, the lower global subdifferential satisfies standard properties for subdifferential operators. Finally, two applications in nonconvex nonsmooth optimization are given: necessary and sufficient optimality conditions for a point to be local minima with and without constraints, and a revisited characterization for nonsmooth quasiconvex functions.

Keywords: Nonsmooth analysis; Global derivatives; Global subdifferentials; Nonconvex optimization; Local minima; 90C30; 90C26 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-020-00981-1

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