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.

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.

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.

考虑电压-无功调节的台区互联装置规划方法

伴随分布式能源广泛接入低压配电网,其对配电网运行灵活性和消纳能力的要求不断提高。利用低压柔性互联装置将独立运行的低压配电台区分区互联,避免传统电压调节和无功补偿装置频繁动作。考虑到柔性互联装置造价昂贵,协同传统电压-无功调节装置,文中提出低压柔性互联装置的选址定容规划方法。首先,分析低压柔性互联装置拓扑和运行方式,建立其潮流模型。其次,建立低压柔性互联装置优化配置的双层规划模型,上层规划以年综合费用最小为目标,下层规划考虑电压-无功协调控制时间序列模型,以运行成本和电压偏差最小为目标,基于粒子群优化算法和混合整数二阶锥规划算法交替求解,得出配电系统最优柔性互联方案和最优运行方式。最后,在IEEE 33节点系统上进行实例分析,验证该双层规划算法的有效性。结果表明,所提方法能有效减少柔性互联装置的过度布置,同时减少由分布式能源频繁波动造成的运行成本。将模型凸化并线性化的方法明显提高了求解效率。

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.

基于自编码器-受限时序卷积网络的数据驱动配电网无功优化策略

配电网中可再生能源渗透率的提高带来了频繁的电压越限问题。作为一种被广泛研究的方法,无功优化方法已经成功应用到配电网中以降低网损、优化电压质量。该文提出一种基于自编码器-受限时序卷积网络的新型数据驱动配电网无功优化策略,该策略通过3个阶段来协调光伏逆变器、电容器组等多种多时间尺度的无功调节设备。首先,将无功优化问题建模为混合整数二阶锥规划问题,求解出历史最优无功调度策略;然后,使用历史运行数据和最优策略训练所提网络模型,并通过矫正层规避不合理结果;在实际运行中,训练好的模型依据系统测量值给出无功优化策略以应对配电网的波动。最后,通过改进IEEE 33节点算例仿真实验验证,所提方法能够达到混合整数二阶锥模型98.80%的准确度而仅消耗其7.14%的时间;与其他流行的深度学习方法相比,具有更佳的性能和更好的实用性。

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.

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Mohr-Coulomb准则和二阶锥规划技术的轴对称自适应下限有限元法

轴对称Mohr-Coulomb准则屈服面的角点问题导致其在数值计算中存在困难,如何高效处理该屈服准则一直是极限分析下限有限元法的重要内容。首先,引入完全塑性假定将轴对称Mohr-Coulomb准则转化为1组不等式约束和3个线性等式约束;然后,将不等式约束直接转化为二阶锥约束,避免了对角点进行光滑近似处理;最后,将基于Mohr-Coulomb准则的轴对称极限分析下限有限元计算模型转化为具有较高计算效率的二阶锥规划数学优化模型。极限分析下限有限元法采用的线性应力单元难以精确模拟破坏区域的应力变化,单元的分布形式对计算精度存在较大影响。因此提出一种基于单元应力的网格自适应加密策略,通过判断单元内节点应力接近屈服的程度,自动识别破坏区域待加密的单元,实现对破坏区域应力分布的精确模拟,进而能够以较少单元获得高精度下限解。通过分析圆形基础承载力及竖向锚板极限抗拔力等典型轴对称岩土工程稳定性问题,表明了所提方法具有较高计算效率及计算精度,具有一定的理论价值和应用前景。

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。

考虑热网潮流的区域热-电综合能源系统协同优化配置研究

区域热-电综合能源系统作为连接跨区域和用户侧综合能源系统的“桥梁”,如何协同其设备配置与系统运行是值得关注的问题。首先,研究建立了考虑流向可变量调节运行方式下的热网模型,通过松弛结合罚函数的方式将其转化为二阶锥形式;进一步结合其他设备及电网潮流模型建立了协同优化配置模型,该模型下的设备配置策略能够同时优化多种设备接入节点的位置及其配置容量。算例结果表明:与传统配置策略相比,同时考虑设备容量及节点位置的配置策略能够减少设备容量配置冗余,降低规划及运行综合成本;流向可变的热网模型能提供更灵活的运行方式以增加设备配置的灵活性,得到成本更低的配置方案。

极限下限分析的区域光滑径向点插值法

极限分析的高效数值计算方法在结构设计和安全评定中具有非常重要的作用.为了更加有效地求解极限分析问题,将区域光滑径向点插值法与二阶锥规划相结合,提出了理想弹塑性结构极限下限分析的一种新方法.将问题域离散为简单的三角形背景单元,每个单元进一步划分成若干个光滑域.为了将复杂的域积分转化为简单的边界积分,并且避免计算形函数的导数,采用广义梯度光滑技术对每个光滑域进行应变光滑处理.由于径向点插值法构造的形函数满足Kronecker delta性质,本质边界条件可以直接施加.依据下限定理,在满足以等效积分弱形式表达的自平衡应力场平衡条件的基础上,用二阶锥规划成功构建了极限分析下限法的计算模型,从而可方便地通过基于原始-对偶内点法的数学规划求解器MOSEK直接求解该问题.数值算例结果表明,本文所提方法有效地克服了维数障碍问题,具有较高的计算精度,并且计算结果对网格畸变十分不敏感.

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。

含电动汽车的主动配电网多目标分层优化调度

为了协调电动汽车车主和主动配电网2个不同主体之间的利益关系,针对电动汽车接入后主动配电网的优化调度问题,文中提出一种考虑电动汽车充电综合满意度和主动配电网运行效益的多目标分层优化方法。上层模型注重最大化电动汽车车主的充电利益,采用归一化法向约束法求解电动汽车的最优充放电计划,并将其输入下层优化模型。下层模型旨在最大化主动配电网的运行效益,根据电动汽车的充放电计划调整可控分布式电源的输出功率,采用二阶锥松弛转换法和带权极小模理想点法求解该非线性多目标问题。仿真结果表明,所提含电动汽车的主动配电网多目标分层优化方法能够在促使电动汽车充电综合满意度超过0.9的同时,减少有功网损约94.12%、运行成本约30.90%,实现电动汽车车主和主动配电网的双赢。

基于凸包理论的含风电电力系统负荷恢复方案优化

大停电事故后,合理的负荷恢复策略对加快电力系统恢复、减少停电损失具有重要意义。针对标准交流潮流方程的非凸性导致负荷恢复模型求解效率低的问题,提出了基于凸包理论的含风电电力系统负荷恢复方案优化方法。首先,简要介绍了凸包理论以及非线性函数的凸包构建方法。其次,针对风电出力的不确定性,采用条件风险价值理论处理风电波动带来的风险,进而建立了直角坐标系下基于凸包理论的电力系统负荷恢复二阶锥优化模型,其中,交流潮流方程中的非线性项采用凸包表达。针对无法精确确定凸包参数的问题,提出了基于迭代更新的参数优化方法,减少因凸包引入的松弛误差。所提出的模型为混合整数二阶锥规划模型,可采用商业求解器高效求解。最后,采用IEEE 39节点系统和改进的广东电力系统验证了所提出模型的有效性。

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.

考虑闭式潮流优化分布的主动配电网供电恢复方法

主动配电网具有灵活的调节能力和快速可靠的运行能力,但柔性多状态开关(SOP)、分布式电源等多种设备的存在,使供电恢复模型复杂,需要研究故障后供电恢复快速决策方法。提出了一种考虑闭式潮流优化分布的主动配电网负荷恢复方案快速决策方法。模拟故障切除后配电网所有联络开关闭式运行状态,基于二阶锥规划求解最优潮流,退出电压低、传输功率小的线路,形成利于供电恢复的配电网含SOP良性网络拓扑。建立基于负荷的功率因数与分级负荷权重的负荷恢复模型,制定负荷供电恢复方案,保证失电负荷严格按优先级获得最大的恢复水平。通过IEEE33、IEEE69节点配电系统进行算例分析,结果表明所提方法能兼顾计算的准确性和快速性。

考虑交通流量和用户行为不确定性的加氢站选址优化模型

加氢站是氢能产业发展的重要基础设施,其布局选址对于氢能在交通领域的推广应用至关重要。为此,提出一种加氢站的选址优化方法。首先,分别以运营商追求捕获交通流量最大化、客户追求获得加氢服务可能性最大化为上、下层目标函数构建了双层规划模型,并引入机会约束规划理论处理了交通流量的不确定性。该模型考虑了客户路径选择的行为特性,能够为交通流量不确定性下的加氢站选址提供重要借鉴。其次,利用KKT条件和确定性等价将所提机会约束双层规划模型转化为了单层的混合整数二阶锥规划问题以实现高效求解。最后,为验证该模型的有效性,以长三角地区交通网络为案例进行了仿真分析。

宽带共形阵基于SRV约束的自适应波束设计

自适应波束形成可以有效抑制非期望信号方向上的干扰信号。针对采用节拍延迟线(Tapped Delay Line,TDL)结构和复数加权系数的宽带共形阵,本文提出一种基于空间响应偏差SRV(Spatial Response Variation)约束的自适应频率不变波束形成器(Frequency Invariant Beamformer,FIB)优化设计方法。该自适应FIB在参考频率上保持预测信号方向无偏响应以及旁瓣级恒定这2个限制条件下,根据对波束形成器输出功率值与平均空间响应偏差值这2项的加权和进行最小化处理的准则进行设计。通过将这种FIB设计问题转化为标准二阶锥规划(Second Order Cone Programming,SOCP)形式后,可以采用内点方法对其进行有效求解。仿真结果验证了本文方法对于宽带共形阵自适应FIB设计的有效性。