Duality and optimality conditions for constrained vector optimization problem on Riemannian manifolds

G. Ruiz Garzón, R. Osuna Gómez, A. Rufián Lizana, B. Hernández Jiménez, J. Ruiz Zapatero

Numerous optimization problems cannot be solved in linear spaces and need of a more general treatment through Riemannian manifolds. Optimization problems with nonconvex objective functions can be written as convex optimization problems by endowing the space with an appropriate Riemannian metric. This work characterizes functions for which every Karush-Kuhn-Tucker vector critical point is an efficient solution of constrained vector optimization problem on Riemannian manifolds. Moreover, a study of the Mond-Weir Dual Problem for the aforesaid problem is undertaken, proving its weak and converse duality results.

Keywords: generalized convexity, Riemannian manifolds, efficient solutions, duality

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