在传感器网络定位问题中,利用接收信号强度RSSI(Received Signal Strength Indication)的定位方法存在着接收信号传播不稳定,定位精度较低的问题。为解决该问题,提出了一种基于阈值Nesterov加速梯度下降NAGT(Nesterov Accelerated Gradi...在传感器网络定位问题中,利用接收信号强度RSSI(Received Signal Strength Indication)的定位方法存在着接收信号传播不稳定,定位精度较低的问题。为解决该问题,提出了一种基于阈值Nesterov加速梯度下降NAGT(Nesterov Accelerated Gradient Descent with Threshold)的RSSI定位算法。算法引入Nesterov思想,不断更新寻优动量,以达到损失函数最小,从而求取对应的未知基站坐标,通过增设阈值,降低了算法陷入局部最优的概率。经仿真比较分析,NAGT方法相对于粒子群算法与随机梯度法,在定位精度与效率上有着较为明显的优势。展开更多
This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the fea...This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.展开更多
In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps....In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.展开更多
This paper illustrates the efficacy of using accelerated gradient descent schemes for minimizing a uniaxially constrained Landau-de Gennes model for nematic liquid crystals.Three(alternating direction)minimization sch...This paper illustrates the efficacy of using accelerated gradient descent schemes for minimizing a uniaxially constrained Landau-de Gennes model for nematic liquid crystals.Three(alternating direction)minimization schemes are applied to a structure preserving finite element discretization of the uniaxial model:a standard gradient descent method,the“heavy-ball”method,and Nesterov’s method.The performance of the schemes is measured in terms of the number of iterations required to obtain the equilibrium state,as well as the total computational time(wall time).The numerical experiments clearly show that the accelerated gradient descent schemes reduce the number of iterations and computational time significantly,despite the hard uniaxial constraint that is not“smooth”when defects are present.Moreover,our results show that accelerated schemes are not hindered when combined with an alternating direction minimization algorithm and are easy to implement.展开更多
文摘在传感器网络定位问题中,利用接收信号强度RSSI(Received Signal Strength Indication)的定位方法存在着接收信号传播不稳定,定位精度较低的问题。为解决该问题,提出了一种基于阈值Nesterov加速梯度下降NAGT(Nesterov Accelerated Gradient Descent with Threshold)的RSSI定位算法。算法引入Nesterov思想,不断更新寻优动量,以达到损失函数最小,从而求取对应的未知基站坐标,通过增设阈值,降低了算法陷入局部最优的概率。经仿真比较分析,NAGT方法相对于粒子群算法与随机梯度法,在定位精度与效率上有着较为明显的优势。
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)Scientific Research Project of Hezhou University(Grant Nos.2014YBZK06 and 2016HZXYSX03)
文摘This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.
文摘In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasible interior-point methods.
基金supported in part by NSF grant DMS-1555222(CAREER).
文摘This paper illustrates the efficacy of using accelerated gradient descent schemes for minimizing a uniaxially constrained Landau-de Gennes model for nematic liquid crystals.Three(alternating direction)minimization schemes are applied to a structure preserving finite element discretization of the uniaxial model:a standard gradient descent method,the“heavy-ball”method,and Nesterov’s method.The performance of the schemes is measured in terms of the number of iterations required to obtain the equilibrium state,as well as the total computational time(wall time).The numerical experiments clearly show that the accelerated gradient descent schemes reduce the number of iterations and computational time significantly,despite the hard uniaxial constraint that is not“smooth”when defects are present.Moreover,our results show that accelerated schemes are not hindered when combined with an alternating direction minimization algorithm and are easy to implement.
