Geodesic B -Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

Sheng-lan Chen, Nan-Jing Huang and Donal O'Regan

Journal of Applied Mathematics, 2014, vol. 2014, 1-12

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:524698

DOI: 10.1155/2014/524698

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