A Study of Generalized Invex Functions on Riemannian Manifold

Jana, S.; Nahak, C.

doi:10.1007/978-81-322-2452-5_3

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2018

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“…Zou et al [32] introduced the classical Penot generalized directional derivative and Clarke's generalized gradient and used these to discuss the first and second order necessary and sufficient conditions for a minimum point of the nonlinear programming problem. Recently, Jana and Nahak [13] obtained the optimality conditions for the nonlinear optimization problem under generalized invexities on a Riemannian manifold.…”

Section: Introductionmentioning

confidence: 99%

Roughly geodesic B - r-preinvex functions on Cartan Hadamard manifolds

Khan¹,

Ismail²

2018

FU Math Inform

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In this article, we introduce a new class of functions called roughly geodesic B????r????preinvex on a Hadamard manifold and establish some properties of roughly geodesic B - r-preinvex functions on Hadamard manifolds. It is observed that a local minimum point for a scalar optimization problem is also a global minimum point under roughly geodesic B-r- preinvexity on Hadamard manifolds. The results presented in this paper extend and generalize the results appeared in the literature.

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Section: Introductionmentioning

confidence: 99%