Matrix Optimization Problem Involving Group Sparsity and Nonnegativity Constraints

In this paper, we consider the matrix optimization problem with group sparsity and nonnegativity constraints. We analyze the optimality conditions and develop two matrix-based improved iterative hard thresholding algorithms for the problem, using the projected gradient method with the Armijo-type stepsize rule and the fixed stepsize, respectively. We then prove that the whole sequence generated by each of the proposed algorithm converges to a local minimizer of the optimization problem and establish the linear convergence rates as well as the iteration complexity results under mild conditions. Finally, numerical results are reported to demonstrate the usefulness of this type of problem and the efficiency of the proposed algorithms.