Geodesicb-preinvex functions and multiobjective optimization problems on riemannian manifolds
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Chen, Sheng-lan; Huang, Nan-Jing; O'Regan, Donal (2014). Geodesicb-preinvex functions and multiobjective optimization problems on riemannian manifolds. Journal of Applied Mathematics ,
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.