现代变分分析可以看成经典的变分法和凸优化的自然产物，它研究凸和非凸函数，集值映射的广义可微性，凸和非凸集切锥和法锥的几何性质以及优化问题的敏感性和稳定性等。本项目以变分分析为工具研究两类结构非凸优化问题。这些问题在信号过程、图像处理、统计分析和机器学习中有广泛应用背景。项目旨在综合运用变分分析、凸优化和矩阵优化的知识探讨两类优化问题的稳定点、最优性条件和约束品性; 针对问题的结构特点设计合理的优化算法，利用变分分析的理论研究算法的收敛性和复杂度。

Modern variational analysis can be viewed as an outgrowth of the calculus of variations and convex optimization, where deal with generalized differentiation of (convex and nonconvex) functions, set-valued mapping and the geometry of tangent and normal cones of (convex and nonconvex) sets, and also the sensitivity and stability analysis of optimization problems and others. In this project, we shall explore two classes structured nonconvex optimization problems based on variational analysis. These problems have wide applications background in signal processing, image recovery, machine Learning and statistics. The aim of this project is to study stationary point, optimality conditions and constraint qualifications of these two kinds of optimization problems by using variational analysis, convex optimization and matrix optimization, to construct reasonable algorithms for solving these problems, and to discuss the convergence and complexity of the methods.