TY - JOUR
T1 - A First-Order Splitting Method for Solving a Large-Scale Composite Convex Optimization Problem
AU - Tang , Yuchao
AU - Wu , Guorong
AU - Zhu , Chuanxi
JO - Journal of Computational Mathematics
VL - 5
SP - 666
EP - 688
PY - 2019
DA - 2019/03
SN - 37
DO - http://doi.org/10.4208/jcm.1808-m2018-0027
UR - https://global-sci.org/intro/article_detail/jcm/13040.html
KW - Forward-backward splitting method, Primal-dual, Dual, Proximity operator.
AB - <p style="text-align: justify;">In this paper, we construct several efficient first-order splitting algorithms for solving
a multi-block composite convex optimization problem. The objective function includes a
smooth function with a Lipschitz continuous gradient, a proximable convex function that
may be nonsmooth, and a finite sum composed of a proximable function and a bounded
linear operator. To solve such an optimization problem, we transform it into the sum
of three convex functions by defining an appropriate inner product space. Based on the
dual forward-backward splitting algorithm and the primal-dual forward-backward splitting
algorithm, we develop several iterative algorithms that involve only computing the gradient
of the differentiable function and proximity operators of related convex functions. These
iterative algorithms are matrix-inversion-free and completely splitting algorithms. Finally,
we employ the proposed iterative algorithms to solve a regularized general prior image
constrained compressed sensing model that is derived from computed tomography image
reconstruction. Numerical results show that the proposed iterative algorithms outperform
the compared algorithms including the alternating direction method of multipliers, the
splitting primal-dual proximity algorithm, and the preconditioned splitting primal-dual
proximity algorithm.</p>