A Proximal-proximal Majorization-minimization Algorithm For Large-scale Nonconvex Sparse Quantile Regression Problems

Nonconvex quantile regression is a useful tool for analyzing large-scale data.However,the computation of nonconvex quantile regression problems has not been completely solved,due to the non-smoothness and nonconvexity of the objective function.This thesis proposes a proximal-proximal majorization-minimization(PPMM)algorithm for large-scale nonconvex sparse quantile regression problems.This thesis reformulates the nonconvex quantile regression problem to difference of convex(DC)functions and apply the sequential convex approximation method to solve problem.For the dual problem,the Proximal Point algorithm(PPA)is used to solve the inner problem,and the semismooth Newton(SSN)method is used to solve the sub-problems.The biggest difficulty that the algorithm overcomes is the singular problem of generalized Jacobian in dealing with inner problem.In addition,this thesis employs the Kurdyka-(?)ojasiewicz(KL)property to analyze the convergence and convergence order of the PPMM algorithm,and also proves that the point sequence generated by the algorithm converges to a d-stationary point.