Numerical Methods for Non-Smooth Optimization

非光滑优化问题涉及目标或约束处处不可微的问题。术语结构化非光滑优化意味着问题的特定非光滑性质是已知的。一个特别有趣的类在许多应用中反复出现：涉及矩阵特征值的问题。该项目主要关注特征值优化的各个方面，包括半定规划、拟凸特征值优化和非lipschitz特征值优化。目标有四个方面：开发快速、健壮的数值算法；最优性条件与算法收敛的理论问题分析开发可供一般科学界使用的软件；并应用于解决实践中出现的有趣的重要问题。

Nonsmooth optimization problems involve objectives or constraints which are not differentiable everywhere. The term structured nonsmooth optimization means that the specific nonsmooth nature of the problem is known. One especially interesting class repeatedly arises in many applications: problems involving eigenvalues of matrices. The project primarily focuses on various aspects of eigenvalue optimization, including semidefinite programming, quasiconvex eigenvalue optimization, and non-Lipschitz eigenvalue optimization. The goal is fourfold: the development of fast, robust numerical algorithms; analysis of theoretical questions concerning optimality conditions and algorithm convergence; development of software which can be used by the general scientific community; and application to the solution of important interesting problems which arise in practice.