Weak Sharp Minima on Riemannian Manifolds
Weak Sharp Minima on Riemannian Manifolds
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DOI：
10.1137/09075367x
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发表时间：
2011-10
期刊：
影响因子：
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通讯作者：
Chong Li;B. Mordukhovich;Jinhua Wang;J. Yao
中科院分区：
文献类型：
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作者：
Chong Li;B. Mordukhovich;Jinhua Wang;J. Yao
This is the first paper dealing with the study of weak sharp minima for constrained optimization problems on Riemannian manifolds, which are important in many applications. We consider the notions of local weak sharp minima, boundedly weak sharp minima, and global weak sharp minima for such problems and establish their complete characterizations in the case of convex problems on finite-dimensional Riemannian manifolds and Hadamard manifolds. A number of the results obtained in this paper are also new for the case of conventional problems in finite-dimensional Euclidean spaces. Our methods involve appropriate tools of variational analysis and generalized differentiation on Riemannian and Hadamard manifolds developed and efficiently implemented in this paper.
