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Abstract In this paper, a notion of generalized gradient on Riemannian manifolds is considered and a subdifferential calculus related to this subdifferential is presented. A characterization of the… (More)
The concept of a geodesic invex subset of a Riemannian manifold is introduced. Geodesic invex and preinvex functions on a geodesic invex set with respect to particular maps are defined. The relation… (More)
Abstract A nonsmooth multiobjective continuous-time problem is introduced. We establish the necessary and sufficient optimality conditions under generalized convexity assumptions on the functions… (More)
Abstract We consider a nonsmooth vector optimization continuous-time problem. We establish weak and strong duality theorems under generalized convexity assumptions.
Prox-regular subsets of Riemannian manifolds are introduced. A characterization of prox-regular sets based on the hypomonotonicity of the truncated limiting normal cone is obtained. Moreover, some… (More)
In 1929 George Birkhoff  showed the existence of an entire function f on C with the remarkable property that its translates approximate every entire function. That is, for each entire function g,… (More)
Abstract Various concepts of invariant monotone vector fields on Riemannian manifolds are introduced. Some examples of invariant monotone vector fields are given. Several notions of invexities for… (More)
We present the notion of weakly metrically regular functions on manifolds. Then, a sufficient condition for a real valued function defined on a complete Riemannian manifold to be weakly metrically… (More)
We introduce a concept of generalized invexity for the nonsmooth continuous time optimization problems, namely, the concept of Karush-Kuhn-Tucker (KKT) invexity. Then, we prove that this notion is… (More)
We show that the injective Kobayashi-Royden differential metric, as defined by Hahn, is upper semicontinous.