A Riemannian Conjugate Gradient Algorithm with Implicit Vector Transport for Optimization on the Stiefel Manifold

Harry F. Oviedo(harry.oviedocimat.mx)
Hugo Lara(hugo.lara.urdanetaufsc.b)

Abstract: In this paper, a reliable curvilinear search algorithm for solving optimization problems over the Stiefel manifold is presented. This method is inspired by the conjugate gradient method, with the purpose of obtain a new direction search that guarantees descent of the objective function in each iteration. The merit of this algorithm lies in the fact that is not necessary extra calculations associated to vector transport. To guarantee the feasibility of each iteration, a retraction based on the QR factorization is considered. In addition, this algorithm enjoys global convergence. Finally, two numerical experiments are given to confirm the effectiveness and efficiency of presented method with respect to some other state of the art algorithms.

Keywords: optimization on manifolds, Stiefel manifold, conjugate gradient method, vector transport.

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: report number 1, Mathematics Research Center, CIMAT A.C. Guanajuato, Mexico. February/2018.

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Entry Submitted: 02/24/2018
Entry Accepted: 02/24/2018
Entry Last Modified: 02/24/2018

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