Nonsmooth Optimization in Constrained Spline Interpolation

基于标准微积分的传统方法可能不适用于具有约束的优化问题;然而，这些问题可以重新表述为需要特殊处理的非光滑问题。本项目旨在从非光滑优化的角度探讨约束样条插值和逼近中的几个重要问题。这项研究建立在申请人及其合作者最近在凸最佳插值方法方面取得的突破基础上，预计将为牛顿型方法提供基础理论，这些方法用于数据拟合和曲线曲面设计中的大量应用。

Traditional methods based on standard calculus may not work for optimization problems with constraints; however, such problems can be reformulated as nonsmooth problems that need special treatment. The project aims to approach several important problems in constrained spline interpolation and approximation, from the perspective of nonsmooth optimization. The research, which builds upon a recent breakthrough in the approach to the convex best interpolation by the applicant and his collaborators, is expected to provide fundamental theory for Newton-type methods being used for these problems with a vast number of applications in data fitting and curve and surface design.