TITLE:
Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces
AUTHORS:
Akachukwu Offia, Ugochukwu Osisiogu, Theresa Efor, Friday Oyakhire, Monday Ekhator, Friday Nkume, Sunday Aloke
KEYWORDS:
Real Banach Spaces, Pseudo-Convex Functions, Pseudo-Monotone Maps, Sub-Differentials, Lower Semi-Continuous Functions and Approximate Mean Value Inequality
JOURNAL NAME:
Open Journal of Optimization,
Vol.12 No.3,
September
14,
2023
ABSTRACT: In
this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex
subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of
non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower
semi-continuous pseudo-convex functions on real Banach spaces.