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The paper addresses the problem of optimizing a class of composite functionson Riemannian manifolds and a new first order optimization algorithm (FOA) witha fast convergence rate is proposed. Through the theoretical analysis for FOA,it has been proved that the algorithm has quadratic convergence. Theexperiments in the matrix completion task show that FOA has better performancethan other first order optimization methods on Riemannian manifolds. A fastsubspace pursuit method based on FOA is proposed to solve the low-rankrepresentation model based on augmented Lagrange method on the low rank matrixvariety. Experimental results on synthetic and real data sets are presented todemonstrate that both FOA and SP-RPRG(ALM) can achieve superior performance interms of faster convergence and higher accuracy.

Fast Optimization Algorithm on Riemannian Manifolds and Its Application in Low-Rank Representation