Greatest Descent Algorithms in Unconstrained Optimization

We show that, for an unconstrained optimization problem, the long-term optimal trajectory consists of a sequence of greatest descent directions and a Newton method in the final iteration. The greatest descent direction can be computed approximately by using a Levenberg-Marquardt like formula. This implies the view that the Newton method approximates a Levenberg-Marquardt like formula at a finite distance from the minimum point, instead of the standard view that the Levenberg-Marquadt formula is a way to approximate the Newton method. With the insight gained from this analysis, we develop a two-dimensional version of a Levenberg-Marquardt like formula. We make use of the two numerically largest components of the gradient vector to define here new search directions. In this way, we avoid the need of inverting a high-dimensional matrix. This reduces also the storage requirements for the full Hessian matrix in problems with a large number of variables. The author thanks Mark Wu, Professors Sanyang Liu, Junmin Li, Shuisheng Zhou and Feng Ye for support and help in this research as well as the referees for helpful comments.     

Used digital speckle correlation method to realize orientation function of optical mouse

Used digital speckle correlation method (DSCM) to realize orientation function of optical mouse is researched. The experiment is designed to obtain the dynamic speckle patterns which are shot by CCD, then the DSCM is used to process the sequential images and also the experiment is simulated. The experimental results show the DSCM can confirm orientation function of the optical mouse, and have a good agreement with the simulation results, and the resolution we obtained is higher than the resolution of mouse on the market.     

MEMS热式风速风向传感器输出性能优化研究

环境测温二极管在工作时受传感器芯片热场影响,常引发MEMS热式风速风向传感器加热电压-风速曲线异常。将其更换为外置测温二极管,并调整其与传感器芯片距离,成功解决了输出曲线异常现象。并在此基础上,优化芯片及外置测温二极管的封装方案,消除了热场的相互干扰和不必要的热损耗,同时保证了外置测温二极管与空气的良好接触。风场测试结果表明,传感器的加热电压-风速曲线变得平滑,且重复性好,风速和风向的测量误差分别在±4%和±4°以内,系统的上电稳定时间大幅缩短至15 s左右。     

Growth and raman scattering of aluminium gallium orthophosphate piezoelectric crystals

A new series of non-ferroelectric crystals, the piezoelectric solid solution aluminium gallium orthophosphate Al_1-xGa_xPO₄ (AGP, 0 < x < 1) system has been successfully developed by a hydrothermal method. The AGP crystal with X = 0.10 shows a phase transition temperature T_−β = 587 ± 3 °C with a cell parameters A = b = 0.49386(3) and C = 1.09563(2) nm. Raman spectra including directional dispersion in AGP are similar to those from -AIPO4 and -quartz crystals, indicating all of them belong to an isomorphic family, the short-range interaction being dominant in AGP. Comparison with -AIPO4 crystals, there exists an apparent red shift of the mode frequency and a smaller TO/LO mode splitting of the E species in the AGP crystals.     

确定信号情况下矢量水听器检测及估计性能研究

在某些场合,例如水下定位、编码通信,信号具有确知脉冲信号特性,声源相对于接收器的方位,可以采用矢量水听器处理来获得。对于确知脉冲信号,本文证明了在各向同性噪声场下,参考声压和振速的相关处理器的方向是声源方位的最大似然方位估计,以及方位估计的克拉美-罗界CRB(Cramer-Rao Bound)。给出了计算机的仿真结果。     

Efficient interval partitioning for constrained global optimization

A new efficient interval partitioning approach to solve constrained global optimization problems is proposed. This involves a new parallel subdivision direction selection method as well as an adaptive tree search. The latter explores nodes (intervals in variable domains) using a restricted hybrid depth-first and best-first branching strategy. This hybrid approach is also used for activating local search to identify feasible stationary points. The new tree search management technique results in improved performance across standard solution and computational indicators when compared to previously proposed techniques. On the other hand, the new parallel subdivision direction selection rule detects infeasible and suboptimal boxes earlier than existing rules, and this contributes to performance by enabling earlier reliable deletion of such subintervals from the search space.     

Conjugate directions method for solving interval linear systems

We propose the interval version of the conjugate directions method, to solve the problem of linear systems, with symmetric and positive definite interval matrix A, and a right-hand side interval vector b. This revised version was published online in June 2006 with corrections to the Cover Date.     

Adaptive nonmonotone line search method for unconstrained optimization

In this paper, an adaptive nonmonotone line search method for unconstrained minimization problems is proposed. At every iteration, the new algorithm selects only one of the two directions: a Newton-type direction and a negative curvature direction, to perform the line search. The nonmonotone technique is included in the backtracking line search when the Newton-type direction is the search direction. Furthermore, if the negative curvature direction is the search direction, we increase the steplength under certain conditions. The global convergence to a stationary point with second-order optimality conditions is established. Some numerical results which show the efficiency of the new algorithm are reported.      

A new algorithm for 2-D DOA estimation

In this paper we present a new algorithm to estimate the 2-D direction of arrival (DOA) of narrowband sources lying in the far field of the array. The array consists of matched co-directional triplets, and can be considered as an extension of the 1-D ESPRIT scenario to 2-D. The proposed approach is simple and direct and does not require a search procedure or initialization. Existing algorithms require a search to match the correct elevation and azimuth angles and are computationally more expensive. This technique automatically pairs the azimuth and elevation angles by marking them. The computational complexity is twice that of 1-D ESPRIT. Simulation results and comparisons with other existing algorithms are presented to demonstrate the performance of the proposed technique.     

亚纯函数涉及小函数的奇异方向

本文研究了平面上亚纯函数的奇异方向.利用角域内Ahlfors-Shimize特征函数和几个已有的关于函数增长性估计的引理,证明了复平面上的零级超越亚纯函数存在一条涉及小函数的T方向.推广了吴昭君和孙道椿给出的结果.