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In this paper, we develop a variant of the well-known Gauss-Newton (GN)method to solve a class of nonconvex optimization problems involving low-rankmatrix variables. As opposed to the standard GN method, our algorithm allowsone to handle general smooth convex objective function. We show, under mildconditions, that the proposed algorithm globally and locally converges to astationary point of the original problem. We also show empirically that the GNalgorithm achieves higher accurate solutions than the alternating minimizationalgorithm (AMA). Then, we specify our GN scheme to handle the symmetric caseand prove its convergence, where AMA is not applicable. Next, we incorporateour GN scheme into the alternating direction method of multipliers (ADMM) todevelop an ADMM-GN algorithm. We prove that, under mild conditions and a properchoice of the penalty parameter, our ADMM-GN globally converges to a stationarypoint of the original problem. Finally, we provide several numericalexperiments to illustrate the proposed algorithms. Our results show that thenew algorithms have encouraging performance compared to existing methods.

Extended Gauss-Newton and ADMM-Gauss-Newton Algorithms for Low-Rank Matrix Optimization