Mathematical Sciences: Studies in Stochastic Optimization

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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.