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, issue 1

Abstract: We introduce a class of functions called geodesic B‐preinvex and geodesic B‐invex functions on Riemannian manifolds and generalize the notions to the so‐called geodesic quasi/pseudo B‐preinvex and geodesic quasi/pseudo B‐invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B‐preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B‐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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https://doi.org/10.1155/2014/524698

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:524698

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