Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2014, Special Issue (2014), Article ID 524698, 12 pages.
Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds
We introduce a class of functions called geodesic -preinvex and geodesic -invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo -preinvex and geodesic quasi/pseudo -invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic -preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic -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.
J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 524698, 12 pages.
First available in Project Euclid: 1 October 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Chen, Sheng-lan; Huang, Nan-Jing; O'Regan, Donal. Geodesic B -Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds. J. Appl. Math. 2014, Special Issue (2014), Article ID 524698, 12 pages. doi:10.1155/2014/524698. https://projecteuclid.org/euclid.jam/1412177577