Mathematical Sciences: Problems in Stochastic Optimization

本课题将从随机优化的角度进行研究， 考虑到具有改进的收敛速度的递归算法， 分布函数辨识过程的渐近性质 参数系统，自适应滤波算法和近似 宽带时滞微分系统的最优控制 噪声 一个有吸引力的和易于实现的随机 分析了相关噪声下的近似算法 流程. 我们的想法是取迭代次数的平均值 中获得 不使用“预白化”的经典近似方法。 处理分布式系统的辨识算法， 将采用函数不变性方法。 所得 属性将有助于更好地了解 衔接问题。 在自适应滤波问题中， 与延迟和投影程序使用“符号”将 研究了 概率为1的充分条件 将产生收敛。 接近最佳控制， 随机扰动下的微分时滞方程， 将通过弱 收敛方法和放松控制的使用。 这些研究的应用范围包括 金融市场的分析，以建设更多 用于雷达的精确软件

This project will study stochastic optimization from the point of view of recursive algorithms with improved convergence speed, asymptotic properties of identification procedures for distributed parameter systems, algorithms for adaptive filtering and nearly optimal controls for differential delay systems with wideband noise. An attractive and easily implementable stochastic approximation algorithm will be analyzed under correlated noise processes. The idea is to take the average of the iterates obtained in the classical approximation approach without using "prewhitening". Dealing with the identification algorithms for distributed systems, a functional invariance approach will be taken. The resulting properties will help to get a better understanding on the rate of convergence issue. In the adaptive filtering problem, algorithms with delays and projection procedures using "sign" will be investigated. Sufficient conditions for with probability one convergence will be derived. Nearly optimal controls for differential delay equations subject to random perturbations and with a small parameter will be developed by means of weak convergence methods and the use of relaxed controls. Applications of these studies are found in areas ranging from the analysis of financial markets to the construction of more precise software for radars.