非线性逼近和优化的适定性

This project is mainly concerned with well posedness of some set approximation problems such as mutually nearest points, mutually furthest points, simultaneous approximation and generalized best approximation, and convergence and point estimate problems of Gauss-Newton methods for nonsmooth optimizations and Newton type methods for nonlinear operator.equation in Banach spaces. A series of results on the generic well posedness.of the above-mentioned best approximation problems and the unified convergence determinations and the generalized point estimate theory are established. Consequently, the well posedness theory for approximation and optimization problems and Smale point estimate theory are improved anddeveloped

本项目运用Banach空间理论，非线性分析及集值分析等近代数学理论研究一般Banach空间中非线性逼近和优化的适定性问题。我们在统一的框架下，刻划了非线性逼近和优化的Bair纲适定性的特征及其对算法收敛分析的作用。该课题的研究不仅促进了逼近论和优化理论的发展，而且也为其它相关学科的研究提出了新的领域，因此，具有相当高的学术价值。