A splitting minimization method on geodesic spaces

João Cruz Neto(jxavierufpi.edu.br)
Barnabé Lima(barnabeufpi.edu.br)
Pedro Soares Júnior (pedrosoaresuespi.br)

Abstract: We present in this paper the alternating minimization method on CAT(0) spaces for solving unconstraints convex optimization problems. Under the assumption that the function being minimize is convex, we prove that the sequence generated by our algorithm converges to a minimize point. The results presented in this paper are the first ones of this type that have been given for theses spaces and alternating type methods. Moreover, the method proposed in this paper is attractive for solving certain range of problems.

Keywords: 65K05, 54E50, 32Q05, 46N10

Category 1: Convex and Nonsmooth Optimization

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Other Topics (Other )

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Entry Submitted: 04/10/2013
Entry Accepted: 04/10/2013
Entry Last Modified: 04/10/2013

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