Solving The Optimal Portfolio Problem Via The Parallel Coordinate Descent Method

We consider the optimal portfolio problems,for which the weights are constrained by l1 and l2 norm.The optimal portfolio problem can be con-sidered as the sum of a smooth convex function and a separable convex function(probably not smooth)minimization problem.The parallel co-ordinate descent method is one of the very effective methods for solving this kind of problems,so we modify the descent direction of parallel coor-dinates method and apply the modified parallel coordinates algorithm to solve the optimal portfolio problems,and prove its global convergence.In this paper,we apply the algorithm to select 12 stocks from the Shanghai and Shenzhen 300 stocks,and use regression to obtain the weights of 12 stocks,then we get the optimal portfolio,and the numerical test is carried out for the Shanghai and Shenzhen 300 index tracking,the results show that the parallel coordinate descent algorithm has the very good effect on the selection of weights.