一类非Lipschitz约束优化的最优性条件

Optimal Conditions for a Class of Non-Lipschitz Constrained Optimizations

本文研究一类具有箱约束的非凸非光滑非Lipschitz最小化模型,它是一类典型的稀疏优化问题,在图像重建、信号处理、变量选择等领域有广泛的应用。该模型的目标函数包含一个非凸、非光滑、非Lipschitz的正则项,约束区域是一个闭凸集。本文给出该模型的一阶和二阶最优性条件,为进一步算法设计和分析提供前提和基础。

A nonconvex, nonsmooth and non-Lipschitz constrained minimization model was studied, which is a typical sparse optimization problem with a wide range of applications in the image reconstruction, signal process- ing, variable selection and other fields. The objective function of the model contains a nonconvex, nonsmooth and non-Lipschitz regularization item, and the feasible area is a closed and convex set. We give the first order and second order optimality conditions for the model. Our results provide the premise and foundation for algorithm de- sign and analysis in the future.