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 contin...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.展开更多
基金The authors would like to thank the two anonymous reviewers for their suggestions and comments to improve the manuscript. This work was supported by the National Natural Science Foundations of China (11401293, 11661056, 11771198)the Natural Science Foundations of Jiangxi Province (20151BAB211010)+1 种基金the China Postdoctoral Science Foundation (2015M571989)the Jiangxi Province Postdoctoral Science Foundation (2015KY51).
文摘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.
文摘基于某电厂2×300 MW亚临界机组,通过设置不同条件的对比试验,从空预器压差、排烟温度以及风机电流的变化,分析应用空预器风量分切技术改造后的运行效益。#2炉空预器应用风量分切技术并更换蓄热元件运行5个月后,A/B侧月平均压差总增幅为9.13/5.19%,A/B侧总平均压差比往年同期分别降低了0.95/1.89 k Pa,降幅为57.23/70.00%;一次风机电流、送风机电流和引风机电流降低了27.5 A;每年可节约成本294.71万元。
