Solving Coefficient Estimation Problem By A Partial Proximal Point Algorithm

We consider a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. The method proposed can be formulated as a novel nuclear norm constrained optimization problem. Then we use the idea of partial proximal point algorithm to compute the problem. In each step of the iteration, we need to solve a semi-smooth sub-problem. We use the conjugation gradient algorithm based on Newton iteration to solve the sub-problem, and give out the convergence analysis of the algorithm. In the part of the numerical experiment, we run the program of the partial proximal point algorithm. And we compare the performance of the partial proximal point algorithm with the VNS method and the interior point method. We show that the partial proximal point algorithm outperforms the VNS method and the interior point method.