AbstractWe introduce a partial proximal point algorithm for solving nuclear norm regularized and semidefinite matrix least squares problems with linear equality constraints. For the inner subproblems, we show that the positive definiteness of the generalized Hessian of the objective function for the inner subproblems is equivalent to the constraint nondegeneracy of the corresponding primal problem, which is a key property for applying a semismooth Newton-CG method to solve the inner subproblems efficiently. N…
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