An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem.

The Fantope-constrained sparse principal subspace estimation problem is initially proposed by Vu et al. (Vu et al., 2013). This paper investigates a semismooth Newton based proximal point (Ppassn) algorithm for solving the equivalent form of this problem, where a semismooth Newton (Ssn) method is utilized to optimize the inner problems involved in the Ppassn algorithm. Under standard conditions, the Ppassn algorithm is proven to achieve global convergence and an asymptotic superlinear convergence rate. Computationally, we derive nontrivial expressions for the Fantope projection and its generalized Jacobian, which are key ingredients for the Ppassn algorithm. Some numerical results on synthetic and real data sets are presented to illustrate the effectiveness of the proposed Ppassn algorithm for large-scale problems and superiority over the alternating direction method of multipliers (ADMM). [ABSTRACT FROM AUTHOR]