Adaptive broadband beamformer for nonuniform linear array based on second order cone programming

Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line （TDL） structure for nonuniform linear array （NLA） is designed according to the rule of minimizing the beamformer＇s output power while keeping the distortionless response （DR） in the direction of desired signal and keeping the constant beamwidth （CB） with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming （SOCP）. The computer simulations are presented which illustrate the effectiveness of our beamformer.

Two new predictor-corrector algorithms for second-order cone programming

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.

A VU-decomposition method for a second-order cone programming problem

A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.

AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

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.

SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH

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.

一种基于MISOCP的复杂绕飞区轨迹优化方法

针对复杂绕飞问题,为提升优化方法的全局寻优能力,提出一种基于混合整数二阶锥规划(MISOCP)的迭代求解算法。首先,定量分析了传统序列凸化方法处理绕飞区(NFZ)约束产生的误差;随后,为消除误差,利用整数变量结合自变量变换将绕飞区约束转化为混合整数线性约束;最后,将原问题转化为MISOCP问题,并设计了迭代算法进行求解。仿真表明,本方法全局寻优能力强,且求解时间仅为GPOPS的20%。对随机生成的复杂绕飞场景,本方法鲁棒性较好,且平均求解时间在10 s量级。

Optimal design and verification of temporal and spatial filters using second-order cone programming approach

Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also presented to optimize these criteria chosen. There are many drawbacks in these methods. In this paper, we introduce a unified framework for optimal design of temporal and spatial filters. Most of the optimal design problems of FIR filters and beamformers are included in the framework. It is shown that all the design problems can be reformulated as convex optimization form as the second-order cone programming （SOCP） and solved efficiently via the well-established interior point methods. The main advantage of our SOCP approach as compared with earlier approaches is that it can include most of the existing methods as its special cases, which leads to more flexible designs. Furthermore, the SOCP approach can optimize multiple required performance measures, which is the drawback of earlier approaches. The SOCP approach is also developed to optimally design temporal and spatial two-dimensional filter and spatial matrix filter. Numerical results demonstrate the effectiveness of the proposed approach.

Second order duality for multiobjective programming with cone constraints

We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.

Nonsingularity in second-order cone programming via the smoothing metric projector

Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker point.Moreover,this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker point.Interestingly,the analysis does not need the strict complementarity condition.

基于SOCP-MKRVM的区域滑坡敏感性分析研究

为了提高相关向量机(RVM)在区域滑坡敏感性评价中的预测能力,提出了基于二阶锥规划的多核相关向量机(SOCP-MKRVM)预测模型。以四川省低山丘陵区为例,选取了8个滑坡孕灾因子训练RVM预测模型,并分别运用受试者工作特征曲线(ROC)和滑坡点密度2种方法对预测结果进行验证。通过与单核RVM模型的对比分析,结果表明:SOCP-MKRVM模型提高了对区域滑坡敏感性的评价能力,预测精度提高到71.33%,ROC曲线下面积达到0.741,滑坡点密度分布更加合理,两低敏感区之和为0.89个/100 km^2,两高敏感区之和为6.54个/100 km^2。

基于SOCP的同时数字多波束干扰技术研究

针对现有方法普遍存在的波束形成算法效率低,难以形成多频点、多方向的同时多波束干扰等缺点,本文提出了一种基于二阶锥规划(SOCP)理论的同时数字多波束干扰形成方法。首先,给出了在不同范数准则条件下干扰多波束优化设计问题的数学描述;然后,以L_2范数准则为例,将干扰多波束设计问题的解析形式转化为相应的SOCP形式。最后,仿真结果表明该方法可以较好地解决相应约束条件下的多频率、多方向雷达目标同时多波束干扰优化设计问题。

基于SOCP的采样矩阵求逆算法分析

为克服自适应波束形成技术中采样矩阵求逆(SMI)算法存在计算繁琐、运算量庞大等缺点,提出一种基于二阶锥规划(SOCP)算法的采样矩阵求逆改进算法,即针对SMI算法中数据块生成权向量的最小二乘模型,将其转化为二阶锥规划(SOCP)形式,然后使用SOCP优化方法能够快速准确地求出最优解.实际仿真结果表明:基于SOCP的SMI改进算法(SOCP-SMI)具有计算精确高、运算量小,且对波束特性的改善效果明显.

基于SOCP的综合能源系统日前调度概率最优能量流

随着能源危机的加重,再电气化成为破解能源发展难题的必然选择。根据电气互联综合能源系统作为再电气化的一种新思路,提出利用二阶锥规划求解综合能源系统日前优化调度概率最优能量流的方法。首先,利用电力系统、天然气系统和能源集线器构建综合能源系统日前调度概率模型;然后,将综合能源系统日前调度概率模型放缩为凸模型;接着,采用点估计法求解综合能源系统日前调度概率最优能量流;最后,利用典型算例在MATLAB上的YALMIP平台验证此算法的正确性与有效性。

基于TDOA测距模型的SOCP和Taylor混合定位方案

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。

一种基于SOCP和IFT的频率-方向不变波束形成方法

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。

基于MISOCP的主动配电网有功无功协调动态优化

针对主动配电网有功无功灵活控制设备协调控制难度大的问题,提出了基于混合整数二阶锥规划(mixed integer second-order cone programming,MISOCP)的主动配电网有功无功协调动态优化方法。首先,建立了包含有功无功灵活控制设备运行约束条件的主动配电网有功无功协调动态优化模型,该模型为混合整数非线性规划(mixed integer nonlinear programming,MINP);其次,为了提高原问题的求解速度,将原问题的MINP模型松弛为易于求取最优解且计算速度快的MISOCP模型,最后,以IEEE 33节点扩展系统进行仿真分析。仿真结果验证了:主动配电网中的有功无功灵活控制设备能大幅降低网络有功损耗,对配网的安全经济运行具有积极意义;MISOCP具有和MINP同等的鲁棒性和最优性,但计算时间大大缩短。

含SOP的交直流混合配电网日前优化调度

为实现交直流混合配电网的高效运行,提出一种含智能软开关的交直流配电网优化调度方法。在对应用于交直流配电网的智能软开关工作原理进行阐述的基础上,建立含智能软开关的交直流配电网优化调度模型。通过线性化和凸松弛技术,将所建立的非线性优化模型转化为二阶锥规划模型,并且采用改进的50节点算例分析验证模型的有效性。算例结果表明,基于所建模型得到的智能软开关运行策略能够降低配电网运行损耗及改善电压越限的情况,显著提高混合配电网的经济性。

基于SOCP理论的子阵级干扰多波束形成方法

大型阵列天线包含成百上千个阵元,如果仍然采用基于阵元级的数字波束形成(DBF),则需要对每一个阵元进行加权处理,会导致系统复杂度很高。若将阵列中相邻的若干个阵元划分为单个子阵,然后对每个子阵进行数字波束形成,系统的复杂度将大大降低。同时针对现有方法难以形成多频点、多方向的同时干扰多波束形成等缺点,论文提出了一种基于二阶锥规划(SOCP)理论的子阵级数字多波束干扰形成方法,仿真结果表明该方法在子阵级可以较好地解决相应约束条件下同时多波束干扰优化设计问题。

基于改进灰狼优化算法的含光伏配电网动态无功优化

针对光伏并网对配电网造成的电压波动、线损增加,以及光伏和负荷出力的不确定性等问题,本文构建基于二阶锥规划的线性凸优化模型,通过控制有载调压变压器和电容器组动作,以及光伏逆变器和静止无功发生器无功补偿能力约束,对日前日内双时间尺度无功优化模型进行动态分析,在简化求解过程的同时加大找到全局最优解的可能性。提出一种基于混沌学习初始化、非线性收敛因子、最优粒子柯西扰动结合蜘蛛猴算法位置更新方式的改进灰狼优化算法,防止算法陷入局部最优并增强其全局搜索能力。最后,运用改进的灰狼优化算法对含光伏的IEEE 33节点系统进行建模仿真,结果表明该算法具有寻优效率高、收敛速度快的优点,验证了算法的可行性和高效性。

基于二阶锥规划SOCP的RSS测距的定位方案

无线传感网中的多类应用均需要准确的定位算法。为了降低定位成本,减少能量消耗,常采用基于接收信号强度RSS(Received Signal Strength)测距,再利用最大似然ML(Maximum likelihood)估计算法求解节点的位置。然而,ML估计为非线性、难以获取全局最优解。为此,提出二阶锥规划SOCP(Second-order Cone Programming)的RSS测距的定位方案。利用SOCP将ML估计转换成SOCP优化问题,再引用最小二乘法简化目标函数,最终建立SOCP表达式,最后利用CVX求解。仿真结果表明,提出的SOCP算法的定位精度比SD/SOCP-2、SDPRSS平均提高了近15%至20%。