This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order a...This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function.Under a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence properties.We also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method.展开更多
基金supported by NSFC Grant 10601043,NCETXMUSRF for ROCS,SEM+2 种基金supported by RGC 201508HKBU FRGssupported by the Hong Kong Research Grant Council
文摘This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function.Under a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence properties.We also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method.
