Dual spectral projected gradient method for generalized log-det semidefinite programming

Log-det semidefinite programming (SDP) problems are optimization problems that often arise from Gaussian graphical models. A log-det SDP problem with an ℓ1-norm term has been examined in many methods, and the dual spectral projected gradient (DSPG) method by Nakagaki et al. in 2020 is designed to efficiently solve the dual problem of the log-det SDP by combining a non-monotone line-search projected gradient method with the step adjustment for positive definiteness. In this paper, we extend the DSPG method for solving a generalized log-det SDP problem involving additional terms to cover more structures in Gaussian graphical models in a unified style. We establish the convergence of the proposed method to the optimal value. We conduct numerical experiments to illustrate the efficiency of the proposed method.