Abstract
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.
Citation
Sheng-lan Chen. Nan-Jing Huang. Donal O'Regan. "Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds." J. Appl. Math. 2014 (SI24) 1 - 12, 2014. https://doi.org/10.1155/2014/524698