TY - JOUR
T1 - A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization
AU - Zheng-Jian Bai, Michael K. Ng & Liqun Qi
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 377
EP - 402
PY - 2009
DA - 2009/02
SN - 2
DO - http://doi.org/10.4208/nmtma.2009.m9002s
UR - https://global-sci.org/intro/article_detail/nmtma/6030.html
KW - Coordinate descent, global convergence, linear convergence rate.
AB - <p style="text-align: justify;">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.</p>