Geodesic \(B\)-preinvex functions and multiobjective optimization problems on Riemannian manifolds
type: Item
instance of: scholarly article
title: Geodesic \(B\)-preinvex functions and multiobjective optimization problems on Riemannian manifolds
zbMATH Open document ID: 1406.90096
DOI: 10.1155/2014/524698
author: Nan-Jing Huang
author: Donal O'Regan
author: Shenglan Chen
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: We introduce a class of functions called geodesic \(B\)-preinvex and geodesic \(B\)-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo \(B\)-preinvex and geodesic quasi/pseudo \(B\)-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic \(B\)-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic \(B\)-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 7010666
Wikidata QID: Q59051896
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/524698
OpenAlex ID: W1963618832
description: scientific article; zbMATH DE number 7010666