A new dual spectral projected gradient method for log-determinant semidefinite programming with hidden clustering structures

This paper proposes a new efficient method for a sparse Gaussian graphical model with hidden clustering structures by extending a dual spectral projected gradient (DSPG) method proposed by Nakagaki et al. (Comput Opt Appl, 76(1):33–68, 2020). We establish the global convergence of the proposed method to an optimal solution, and we show that the projection onto the feasible region can be solved with low computational complexity by using the pool-adjacent-violators algorithm. Numerical experiments on synthetic data and real data demonstrate the efficiency of the proposed method. The proposed method takes 0.91 s to achieve a similar solution to the direct application of the DSPG method which takes 4361 s.