## Taiwanese Journal of Mathematics

### ROUGHLY GEODESIC $B$-INVEX AND OPTIMIZATION PROBLEM ON HADAMARD MANIFOLDS

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 17, Number 3 (2013), 833-855.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499705986

Digital Object Identifier
doi:10.11650/tjm.17.2013.1937

Mathematical Reviews number (MathSciNet)
MR3072264

Zentralblatt MATH identifier
1281.49038

#### Citation

Zhou, Li-wen; Huang, Nan-jing. ROUGHLY GEODESIC $B$-INVEX AND OPTIMIZATION PROBLEM ON HADAMARD MANIFOLDS. Taiwanese J. Math. 17 (2013), no. 3, 833--855. doi:10.11650/tjm.17.2013.1937. https://projecteuclid.org/euclid.twjm/1499705986

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