复合优化问题包括最优化、信号过程、图象处理、机器学习和统计中的很多实际问题， 例如约束优化、最大特征值问题、 矩阵的核范数问题、最小二乘问题和正则化极值问题等都可以用复合优化来描述， 利用凸优化的思想研究这些具体问题是这一研究领域的主要研究方向之一。 本项目旨在以凸分析、变分分析为工具研究复合优化问题的增广Lagrangian对偶理论和方法，正则线性化子问题的稳定性、敏感分析和邻近点方法；并应用一般成果研究特征值优化问题、矩阵完全化问题等。

A wide variety of important optimization problems in signal processing, image recovery, machine Learning and statistics can be formulated in compsite optimization problem, such as constraint optimization problem, maximal eigenvalue optimization, nuclear norm and matrix completion, least squares and regularized minimization problems and so on. Exploring these prbolems via convex optimizaion is one of the main research direction in this field. The aim of this project is to study the augmented Lagrangian duality and method of composite optimization problem, and the stability and sensitivity and proximal point methods of its regularized linearization problem as well as applying the obtained result to study eigenvalue optimization problem and matrix completion problems.