an equivalent integral programming model and a new semidefinite programming relaxation for the max-bisection problem are given . then, we solve the relaxation with a projected gradient algorithm . coupled with the randomized method, an approximate solution of the max-bisection problem is obtained 2.给出图的最大二等分问题的整数规划模型的等价模型及其新的半定规划松弛模型,利用投影梯度算法求解该半定规划松弛模型,然后利用随机扰动算法求得原问题的次优解
and with the results of calculation obtained by the first-order gradient algorithms which is initial value of the neighboring extremal algorithms we can transform the problem into a face to point one, then a good result is attained by the neighboring extremal algorithms . in the end, the course of orbit transfers is depicted 利用梯度法对两点边值问题进行计算,将面对面的问题转化为一个点对点问题,将所得结果作为邻近极值法的初始值并进行精确计算。最后,描绘了最优变轨过程。
in the algorithm level, currently various training algorithms of neural networks, including gradient algorithms, intelligent learning algorithms and hybrid algorithms, are comparatively studied; the optimization principle of bp algorithm for neural networks training is analyzed in detail, and the reasons for serious disadvantages of bp algorithms are found out, moreover, the optimization principle of two kinds of improved bp algorithms is described in a uniform theoretic framework; and the global optimization algorithms of neural networks, mainly genetic algorithm are expounded in detail, it follows that a improved genetic algorithm is proposed; finally the training performances of various algorithms are compared based on a simulation experiment on a benchmark problem of neural network learning, furthermore, a viewpoint that genetic algorithm is subject to " curse of dimension " is proposed 在算法层,本文对目前用于神经网络训练的各种算法,包括梯度算法、智能学习算法和混合学习算法进行了比较研究;对用于神经网络训练的bp算法的优化原理进行了详细的理论分析,找到了bp算法存在严重缺陷的原因,并对其两类改进算法-启发式算法和二次梯度算法的优化原理,在统一的框架之下进行了详尽的理论描述;对神经网络全局优化算法主要是遗传算法进行了详细的阐述,并在此基础上,设计了一种性能改进的遗传算法;最后基于神经网络学习的benchmark问题对各种算法在网络训练中的应用性能进行了仿真研究,并提出了遗传算法受困于“维数灾难”的观点。
in each section, we discuss every method's global convergence properties and numerical behaviors etc . in the second chapter, we develop several new conjugate gradient algorithms, explore their convergence properties and analyze the numerical results . by comparing the numerical results, we can find the advantages of these new algorithms 然后对共轭梯度法理论研究的基础上,得到了几种新的共轭梯度法,并对它们的收敛性进行了分析,证明了新算法的全局收敛性。大量数值试验结果也表明了这些算法的有效性。
based on artificial neural network technique, a regional economic forecasting system, which has been applied to practical regional medium-and long-term economic forecasting in certain city, is designed . a mixed hs-fr conjugate gradient algorithm is applied to the regional economic forecasting system to train the neural networks effectively 将人工神经网络技术应用于地区经济预测领域,设计了一个“基于人工神经网络的地区经济预测系统”,并利用hs-fr共轭梯度算法对网络的学习算法进行了改进。