Steepest descent method with a generalized Armijo search for quasiconvex functions on Riemannian manifolds |
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Authors: | EA Papa Quiroz P Roberto Oliveira |
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Institution: | Department of Systems Engineering and Computer Science, PESC-COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil |
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Abstract: | This paper extends the full convergence of the steepest descent method with a generalized Armijo search and a proximal regularization to solve minimization problems with quasiconvex objective functions on complete Riemannian manifolds. Previous convergence results are obtained as particular cases and some examples in non-Euclidian spaces are given. In particular, our approach can be used to solve constrained minimization problems with nonconvex objective functions in Euclidian spaces if the set of constraints is a Riemannian manifold and the objective function is quasiconvex in this manifold. |
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Keywords: | Steepest descent method Riemannian manifolds Quasiconvex functions |
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