带有抽象约束的稀疏优化问题的最优性条件

Sparsity constrained optimization has been applied widely in signal and image processing, machine learning, pattern recognition and computer vision, and so on. In this project, we consider the sparsity optimization with abstract constraint, and conclude the theoretical results including M-stationary and S-stationary (strong stationary) by utilizing the generalized normal cones; first- and second-order optimality conditions by way of generalized differential; stationary and optimality conditions from the view of disjunctive optimization.

稀疏约束优化问题被广泛应用于信号回收、图像处理、机器学习、图像识别、计算机显像等诸多领域。本项目以带有抽象约束的稀疏优化问题为研究对象，主要内容包括：利用广义法锥刻画M-稳定性和S-稳定性（强稳定性）；利用广义微分计算一阶、二阶广义导数，刻画最优性条件；借鉴分离优化等方法研究稳定性，刻画最优性条件。