Proximal point method for minimizing quasiconvex locally Lipschitz functions on Hadamard manifolds

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• 作者：E.A. Papa Quiroz ; P.R. Oliveira
• 关键词：Proximal point method ; Quasiconvex functions ; Locally Lipschitz functions ; Hadamard manifolds ; Global convergence
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：October, 2012
• 年：2012
• 卷：75
• 期：15
• 页码：5924-5932
• 全文大小：262 K

文摘

In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the sequence generated by the method to a critical point of the function.