Non-monotone Spectral Projected Gradient Method for Semidefinite Program with Log-Determinant and $ell_{1}-$1Norm Terms (New Trends of Numerical Optimization in Advanced Information-Oriented Society)

Abstract

A variant of the spectral projected gradient (SPG) method proposed by Birgin, Martinez and Raydan is proposed to solve semidefinite programs with log-determinant and ell_{1}-norm terms. The SPG is modified in the orthogonal projection of the iterates onto the convex feasible set in order to obtain a cheap computation. Numerical results on the problems considered in the literature confirm that the implementation of the proposed method can be comparably faster than other well-known methods for similar problems.