Numerical Methods for Structured Nonsmooth Optimization

9401136奥弗顿非光滑优化问题涉及的目标或约束不是处处可微的。 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。 本文主要研究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：快速，强大的数值算法的发展;有关最优性条件和算法收敛的理论问题的分析;软件的发展，可用于一般科学界;应用到解决重要的有趣的问题，在实践中出现。 特别感兴趣的应用领域包括组合优化，鲁棒控制和结构分析。 ***

9401136 Overton 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. This work 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; application to the solution of important interesting problems which arise in practice. Application areas of particular interest include combinatorial optimization, robust control and structural analysis. ***