On the supporting quasi-hyperplane and separation theorem of geodesic convex sets with applications on Riemannian manifolds

Li-wen Zhou; Ling-ling Liu; Chao Min; Yao-jia Zhang; Nan-Jing Huang

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arXiv · 2401.13316

On the supporting quasi-hyperplane and separation theorem of geodesic convex sets with applications on Riemannian manifolds

Li-wen Zhou·Ling-ling Liu·Chao Min·Yao-jia Zhang·Nan-Jing Huang

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Abstract

In this paper, we first establish the separation theorem between a point and a locally geodesic convex set and then prove the existence of a supporting quasi-hyperplane at any point on the boundary of the closed locally geodesic convex set on a Riemannian manifold. As applications, some optimality conditions are obtained for optimization problems with constraints on Riemannian manifolds.

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Li-wen Zhou, Ling-ling Liu, Chao Min, Yao-jia Zhang, Nan-Jing Huang. 2024-01-24. On the supporting quasi-hyperplane and separation theorem of geodesic convex sets with applications on Riemannian manifolds. https://arxiv.org/abs/2401.13316

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