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2013 ROUGHLY GEODESIC $B$-INVEX AND OPTIMIZATION PROBLEM ON HADAMARD MANIFOLDS
Li-wen Zhou, Nan-jing Huang
Taiwanese J. Math. 17(3): 833-855 (2013). DOI: 10.11650/tjm.17.2013.1937

Abstract

In this paper, a new class of roughly geodesic $B$-invex sets, quasi roughly geodesic $B$-invex functions and pseudo roughly geodesic $B$-invex functions are introduced and studied on Hadamard manifolds by relaxing the definitions of geodesic convex sets and functions. Some properties of quasi roughly geodesic $B$-invex functions and pseudo roughly geodesic $B$-invex functions are proved on Hadamard manifolds. As applications, some sufficient and necessary conditions for optimal solution of the nonlinear programming problems involving the quasi roughly geodesic $B$-invex functions and the pseudo roughly geodesic $B$-invex functions are given on Hadamard manifolds. The Mond-weir type dual problems for the nonlinear programming problems are also considered on Hadamard manifolds.

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Li-wen Zhou. Nan-jing Huang. "ROUGHLY GEODESIC $B$-INVEX AND OPTIMIZATION PROBLEM ON HADAMARD MANIFOLDS." Taiwanese J. Math. 17 (3) 833 - 855, 2013. https://doi.org/10.11650/tjm.17.2013.1937

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1281.49038
MathSciNet: MR3072264
Digital Object Identifier: 10.11650/tjm.17.2013.1937

Subjects:
Primary: 49J40 , 54H25

Keywords: Hadamard manifold , Mond-weir type dual , nonlinear optimization problem , roughly geodesic $B$-invex function , roughly geodesic $B$-invex set

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 3 • 2013
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