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Steepest descent method for quasiconvex minimization on Riemannian manifolds

Erik Papa Quiroz (erik***at***cos.ufrj.br)
E. M. Quispe (mariss***at***cos.ufrj.br)
P. Roberto Oliveira (poliveir***at***cos.ufrj.br)

Abstract: This paper extends the full convergence of the steepest descent algorithm with a generalized Armijo search and a proximal regularization to solve quasiconvex minimization problems defined on complete Riemannian manifolds. Previous convergence results are obtained as particular cases of our approach and some examples in non Euclidian spaces are given.

Keywords: Steepest descent method; Riemannian manifolds; Quasiconvex functions.

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: J. Math. Anal. Appl. 341 (2008) 467-477

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Entry Submitted: 05/10/2006
Entry Accepted: 05/10/2006
Entry Last Modified: 05/15/2008

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