Mathematical Sciences: Studies in Stochastic Optimization

将开展解析和数值随机优化研究。要分析的具体问题包括：具有宽带噪声和未知参数过程的系统的近最优性，制造系统通过随机优化逼近最优阈值，分布参数系统的最小二乘辨识算法中近似误差序列的抽样分布，以及平滑随机逼近/优化算法的渐近最优收敛速度。制造系统中的许多问题涉及宽带噪声和未知参数过程。因此，人们有兴趣从数学的角度来理解这种随机过程。通过将最优策略应用于实际物理系统的适当近似，将开发出接近最优的策略。在许多生产计划问题中，最优控制都是用某些阈值来描述的，这些阈值便于日常操作。然而，这些值的选择通常是基于临时考虑或以前的经验，实际上可能远远不是最佳的。本研究的第二部分致力于设计一种系统的方法来寻找最佳阈值。

Research into analytical and numerical stochastic optimization will be carried out. Specific problems to be analyzed include: near optimality of systems with wideband noise and an unknown parameter process, approximation of optimal threshold values via stochastic optimization for manufacturing systems, sampling distributions of approximate error sequences in least squares identification algorithms for distributed parameter systems, and asymptotically optimal rates of convergence for smoothed stochastic approximation/optimization algorithms. Many problems in manufacturing systems involve wideband noise and unknown parameter processes. Consequently, there is interest in understanding such stochastic processes from a mathematical point of view. By applying an optimal strategy to a suitable approximation of the actual physical system, a near optimal policy will be developed. In many production planning problems, the optimal controls are described by certain threshold values, which are easy to use for daily operation. However, the choice of these values is often based on ad hoc considerations or previous experience and in fact may be far from optimal. The second part of this research is concerned with designing a systematic way of finding the optimal threshold values.