Extended Gauss-Newton and ADMM-Gauss-Newton algorithms for low-rank matrix optimization

In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve class nonconvex optimization problems involving low-rank matrix variables. As opposed standard GN method, our algorithm allows one handle general smooth convex objective function. We show, under mild conditions, that proposed globally and locally converges stationary point original problem. also show empirically achieves higher accurate solutions than alternating minimization (AMA). Then, specify scheme symmetric case prove its convergence, where AMA is not applicable. Next, incorporate into direction multipliers (ADMM) an ADMM-GN algorithm. that, conditions proper choice penalty parameter, Finally, provide several numerical experiments illustrate algorithms. Our results new algorithms have encouraging performance compared existing methods.