一种基于半定松弛规划的到达角定位方法

针对基于到达角的目标辐射源定位系统,提出了一种基于半定松弛规划的定位方程求解方法。主要思想是将噪声元素添加为有用参数,以增加定位方程凸优化的灵活性。先将目标定位的初始非凸二次优化问题转化为非凸半定优化问题,然后松弛到凸优化问题,再对凸优化问题进行求解作为初始复杂问题的近似解,从而得出目标位置估计。文中采用计算机仿真结果证明了这种解法的有效性。     

无源时差定位方程的半定松弛解法

针对基于到达时差量测的多站无源定位系统,提出了一种基于半定松弛的时差定位方程求解方法.该方法首先将关于目标位置估计的非凸二次优化问题转换成等价的非凸半定规划问题,然后通过秩1松弛得到一个凸优化问题,最后对松弛半定规划问题的最优解进行秩1近似,从而提取出最终的目标位置估计.计算机仿真结果表明这种松弛解法可以有效求解目标位置.     

基于半定松弛的时差定位系统优化布站算法

在时差定位系统中,观测站与目标的几何位置关系对定位精度有着重要影响。针对传统布站方法只适用于规则布站区域的不足,本文提出了一种新的可用于不规则布站区域内的近似最优布站算法。该算法所遵循的最优准则是使系统对目标的定位误差椭球体积下限达到最小,通过离散化布站区域将最优布站问题等价为一个组合优化问题,并采用半定松弛方法将难以求解的组合优化问题变换为一个易于求解的半定规划问题,从而得到规定布站区域内的优化布站方案。计算机仿真结果表明,该算法既可以用于规则布站区域也适用于不规则布站区域。     

TSCG算法在图像修复中的应用

霍等人提出了求解大规模无约束优化问题的三维子空间共轭梯度算法（简称为TSCG）,该算法是在一个特殊三维子空间上,通过极小化目标函数的二次近似模型来确定嵌套参数。在温和的假设条件下,证明了该算法对一般非凸函数的全局收敛性,并通过应用在无约束优化问题的数值实验,表明了该算法具有鲁棒性和高效性。在此基础上,文中把该算法运用到添加三种不同噪声的图像修复问题中,表明了该算法在解决这类问题中的性能是稳健且高效的。     

结合CF和PCG搜索的拟牛顿优化算法

针对拟牛顿优化算法求解非线性方程组和无约束优化问题时,需要进行大量的迭代计算的问题。文中提出了一种结合CF和PCG搜索的拟牛顿优化算法,该算法结合CF和PCG搜索的步长因子来得到一种有效的牛顿搜索算法。在强Wolfe准则下的全局收敛性和数值分析结果表明,文中所提出的算法能加快拟牛顿优化算法的求解速度并能得到更高的精度。     

电阻抗成像的修正阻尼最小二乘重建算法

本文给出了一种新的电阻抗成像的图像重建算法,该算法是对Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ类算法的改进。算法根据 目标函数的分析,将以前常用的,对正规方程组的求解。转化为 解一个条件数更好的超定方程组的最小二乘解。理论分析和数值试验都表明,这种新的重建算法较常用的Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ类算法,不仅数值稳定性有较大的提高,而且计算量有所减少,同时这种算法也适用于其他最小二乘问题的求解。     

基于半定松弛的长码DSSS信号扩频波形估计

针对非合作通信中的长码DSSS信号,提出了一种基于半定松弛的扩频波形估计方法,并在确定信号模型下推导了扩频波形估计的CRB.首先推导了长码DSSS信号扩频波形的极大似然估计,由于该极大似然估计为非凸的组合优化问题,提出通过松弛约束条件将其转化为具有多项式计算复杂度的半定规划问题,实现对该极大似然估计问题的近似求解.仿真表明本文提出方法性能优于现有方法,并随着信噪比的提高逐渐逼近CRB.     

多无人机编队异常检测的稀疏优化算法

针对多无人机编队的异常检测问题,为避免多假设检验及概率不等式的复杂性,将异常检测问题转化为一个线性未知参数矢量的辨识过程。在有无异常检测个数的先验条件下,分别构造极大似然辨识问题和非凸的稀疏优化问题,利用最优必要条件求解最优估计值。采用松弛法将非凸稀疏优化规划成易于求解的凸优化问题。针对凸优化问题中的范数形式,分别应用最优必要条件和快速梯度算法来近似估计最优值,并分析快速梯度算法的收敛不等式。最后用仿真算例验证所提方法的有效性。     

训练支持向量机的极大熵方法

支持向量机是基于统计学习理论的结构风险最小化原理提出来的一种新的学习算法,它把模式识别问题建模为一个简单约束的高维二次规划问题。利用Lagrangian对偶方法,把求解二次规划等价为求解低维的无约束不可微优化问题。提出极小化一个严格凸的熵函数来处理不可微问题,得到原二次规划的扰动问题的最优解。数据仿真结果表明该算法在低存储需求下有效提高了大数据量问题的训练学习速度。     

非确知目标先验知识条件下MIMO雷达稳健波形设计

考虑稳健波形优化问题以提高多输入多输出雷达最差条件下参数估计精度。基于最小-最大方法,将初始参数误差模型显式包含进波形优化问题,并基于克拉美-罗界得到稳健波形设计。为求解得到的复杂非线性优化问题,基于哈达玛不等式将其转化为半定规划问题,从而可高效求解。仿真结果表明,与不相关发射波形以及非稳健方法相比,所提方法可显著改善最差条件下参数的估计性能。     

The design of weighted minimax quadrature mirror filters

A technique for converting the constrained nonlinear optimization problem encountered in the design of weighted minimax quadrature mirror filters into an iterative unconstrained nonlinear optimization problem is presented. This renders the design of weighted minimax quadrature mirror filters possible. The technique is very efficient, typically taking about seven iterations to converge. A rapidly converging iterative procedure for solving the above nonlinear unconstrained optimization problem is also presented. This procedure typically requires less than five iterations to converge     

Optimal apportionment of reliability and redundancy in seriessystems under multiple objectives

A multiobjective reliability apportionment problem for a series system with time-dependent reliability is presented. The resulting mathematical programming formulation determines the optimal level of component reliability and the number of redundant components at each stage. The problem is a multiobjective, nonlinear, mixed-integer mathematical programming problem, subject to several design constraints. Sequential unconstrained minimization techniques in conjunction with heuristic algorithms are used to find an optimum solution. A generalization of the problem in view of inherent vagueness in the objective and the constraint functions results in an ill-structured reliability apportionment problem. This multiobjective fuzzy optimization problem is solved using nonlinear programming. The computational procedure is illustrated through a numerical example. The fuzzy optimization techniques can be useful during initial stages of the conceptual design of engineering systems where the design goals and design constraints have not been clearly identified or stated, and for decision making problems in ill-structured situations     

A Unified Review of Optimization

The main objective of this paper is to give a survey of recent automatic optimization methods which either have found or should find useful application in the area of computer-aided network design. Huang's family of algorithms for unconstrained optimization is reviewed. The Fletcher method and the Charalambous family of algorithms for unconstrained optimization, which abandon the "full linear search," are presented. Special emphasis is devoted to algorithms by Bandler and Charalambous on least pth and minimax optimization which can be readily programmed and used. Due to work by Bandler and Charalambous, it is shown how constrained minimax problems can be solved exactly as unconstrained minimax problems by using a new approach to nonlinear programming. The application of minirnax optimization on the design of lumped-distributed active filters, problems for future investigation, and a select list of references are also included.     

DSA guiding template assignment with multiple redundant via and dummy via insertion

As an emerging manufacture technology, block copolymer directed self-assembly (DSA) is promising for via layer fabrication. Meanwhile, redundant via insertion is considered as an essential step for yield improvement. For better reliability and manufacturability, in this paper, we first concurrently consider DSA guiding template cost assignment with multiple redundant via and dummy via insertion. Firstly, by analyzing the structure property of guiding templates, we propose a building-block based solution expression to discard redundant solutions. Then, honoring the compact solution expression, we construct a conflict graph with dummy via insertion, and then formulate the problem to an integer linear programming (ILP). In addition, to optimize the guiding template cost, we incorporate it into the objective of ILP by introducing vertex weight and edge weight in conflict graph. To make a good trade-off between solution quality and runtime, we relax the ILP to an unconstrained nonlinear programming (UNP). Finally, a line search optimization algorithm is proposed to solve the UNP. Experimental results verify the effectiveness of our new solution expression and the efficiency of our proposed algorithm. Specifically, our guiding template cost optimization method can save 18% total guiding template cost.     

Synthesis of antenna arrays with spatial and excitation constraints

Synthesis of antenna arrays subject to spatial and excitation constraints to yield arbitrarily prescribed patterns in both the mean-squared and minimax sense are discussed. The spatial constraints may require that the interelement spacings be greater than a prescribed value or that the element locations lie within a specified region. The excitation constraints are of the form where the current-taper ratio is constrained to be less than or equal to a prescribed value. The technique employed consists of reducing the constrained optimization problem into an unconstrained one by the use of simple transformations of the independent variables. In such cases where explicit transformations are not available, a created response surface technique (CRST) has been used to convert the constrained optimization problem into a series of unconstrained optimizations. The optimization has been carried out using a nonlinear simplex algorithm. Numerical examples are given wherein both the linear and circular arrays are synthesized subject to constraints.     

Optimization of System Reliability by the Sequential Unconstrained Minimization Technique

The reliability of a complex system was optimized by a new approach for implementing the sequential unconstrained minimization technique (SUMT) with the aid of Hooke and Jeeves pattern search and heuristic programming. Two optimization problems were considered. In the first, the system reliability was maximized subject to a nonlinear weight constraint. In the second, the weight of the system was minimized without violating the requirements of the minimal system reliability and the minimum reliability for each component. The sensitivities of the system reliability and that of the system weight to the reliability of each component were determined under optimal conditions.     

Computation of minimum cross entropy spectral estimates: An unconstrained dual convex programming method

The minimum cross entropy spectral analysis procedure (a generalization of maximum entropy spectral analysis) is formulated as a convex programming problem, and its unconstrained dual convex programming problem is shown. In this dual setting the Lagrange multipliers are precisely the dual variables, and the numerical solution values are easily determined by any of a number of nonlinear programming codes. This result vastly simplifies the computation of all such spectral density estimates.     

Design of Coupled Microstrip Lines by Optimization Methods (Short Paper)

The design of two coupled microstrip lines is converted into an optimization problem, which is then solved by two methods of nonlinear mathematical programming. New formulas for calculating the first approximation of the solution, i.e., the starting point of the optimization, are given.     

Optimal Reliability Allocation Under Preventive Maintenance Schedule

This paper considers a series system of components with time-dependent reliability and gives a new formulation of an optimal reliability allocation problem where an optimal preventive maintenance (PM) schedule is determined simultaneously. The importance of this formulation is shown in comparison with a conventional formulation where PM schedule is not taken into account. The optimization problem becomes a nonlinear mixed-integer programming problem. A simple approximate solution algorithm is given on the basis of a nonlinear programming (NLP) algorithm. The procedure is illustrated by use of a numerical example. Though we restrict our attention to the case where a preventive replacement is adopted as a PM policy, a similar discussion is possible for the as-good-as-new repair.     

Separate/joint optimization of error feedback and realization for roundoff noise minimization in a class of 2-D state-space digital filters

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l ₂-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. A numerical example is presented to illustrate the utility of the proposed techniques.