A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorith...A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.展开更多
In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w...In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.展开更多
针对无线传感网络WSNs(Wireless Sensor Networks)的定位问题,提出基于TDOA(Time Different of Arrival)测距模型的SOCP(Second order cone programming)和Taylor混合定位方案,记为SOCP+Taylor。SOCP+Taylor方案首先分析了网络可定位性...针对无线传感网络WSNs(Wireless Sensor Networks)的定位问题,提出基于TDOA(Time Different of Arrival)测距模型的SOCP(Second order cone programming)和Taylor混合定位方案,记为SOCP+Taylor。SOCP+Taylor方案首先分析了网络可定位性,并结合刚论(rigid),提出了评判节点可定位的条件。然后,建立TDOA测距模型,并用最大似然估计建立距离测量值的最大似然函数,再通过松弛约束理论将非凸优问题转换成凸优问题,引入惩罚因子,进而利用SOCP估计节点位置,并将此节点位置作为泰勒级数展开法Taylor迭代的初始值,最后,利用Taylor估计节点的最终位置。在不同参考节点数目以及变化的噪声环境下对算法进行仿真。仿真结果表明,提出的定位方案具有高的定位精度,定位误差逼近于CRLB,同时分析了惩罚因子对定位精度的影响,并确定了惩罚因子的最佳取值区域。展开更多
常规波束形成中主瓣宽度随频率和方向(方位角和俯仰角)变化,进而影响阵列分辨率及波束形成器的整体性能。为实现频率-方向不变波束形成,提高波束形成可靠性,基于约束优化的思想,提出一种基于二阶锥规划(second order cone programming,S...常规波束形成中主瓣宽度随频率和方向(方位角和俯仰角)变化,进而影响阵列分辨率及波束形成器的整体性能。为实现频率-方向不变波束形成,提高波束形成可靠性,基于约束优化的思想,提出一种基于二阶锥规划(second order cone programming,SOCP)和傅里叶逆变换(Inverse Fourier Transform,IFT)的宽带频率-方向不变恒定束宽波束形成方法。方法以均匀矩形平面阵为模型,首先采用SOCP波束优化设计方法得到参考波束,再基于IFT设计出参考方向上的频率不变恒定主瓣波束,最后基于提出的SOCP二维方向不变波束形成新方法实现不同频点上的方向不变恒定主瓣波束。经仿真分析,方法设计的波束在数字频率π/2~π、不同方位角及俯仰角指向15°~50°上均具有束宽较恒定的波束,与基于线阵的恒定束宽波束形成方法相比,提高了波束形成器在实际空间中的可靠性,具有一定的相关工程应用参考价值。展开更多
基金the National Science Foundation(60574075, 60674108)
文摘A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.
基金supported by the National Natural Science Foundation of China(11401126,71471140 and 11361018)Guangxi Natural Science Foundation(2016GXNSFBA380102 and 2014GXNSFFA118001)+2 种基金Guangxi Key Laboratory of Cryptography and Information Security(GCIS201618)Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112 and YQ16112)China
文摘In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.
文摘针对无线传感网络WSNs(Wireless Sensor Networks)的定位问题,提出基于TDOA(Time Different of Arrival)测距模型的SOCP(Second order cone programming)和Taylor混合定位方案,记为SOCP+Taylor。SOCP+Taylor方案首先分析了网络可定位性,并结合刚论(rigid),提出了评判节点可定位的条件。然后,建立TDOA测距模型,并用最大似然估计建立距离测量值的最大似然函数,再通过松弛约束理论将非凸优问题转换成凸优问题,引入惩罚因子,进而利用SOCP估计节点位置,并将此节点位置作为泰勒级数展开法Taylor迭代的初始值,最后,利用Taylor估计节点的最终位置。在不同参考节点数目以及变化的噪声环境下对算法进行仿真。仿真结果表明,提出的定位方案具有高的定位精度,定位误差逼近于CRLB,同时分析了惩罚因子对定位精度的影响,并确定了惩罚因子的最佳取值区域。
