The Optimization For Matrix Function With Non-smooth Regular Term

The matrix function with nonsmooth regular item has many applications,there were some conclusion about the vector function with nonsmooth regular item in[33].When solving these problems,people would like to use gradient descent method to con-vert the problem into linearly constrained nuclear norm minimization prob-lem.Supposing that linearly constrained nuclear norm minimization problem can be solved exactly and accurately,gra,dient descent method is able to achieve the same con-vergence rate as smooth problem,O(k/1).Beck.A and Teboulle.M accelerate the vec-tor model by accelerated gradient descent method in[33],the optimization re-sult was O(k2/1),which is the best result in solving 1 order smooth problem.When talk-ing about linearly constrained nuclear norm minimization problem people usu-ally compute it by Singular Value Thresholding Algorithm[8]or Semi-definite Pro-gramming[45],in this paper,we use the Fixed Point Continuation Iterative Algo-rithm[17]to improve the model.The model can be used to deal with larger ma-trix in less time after changing the algorithm.