一类非Lipschitz约束优化的最优性条件  

Optimal Conditions for a Class of Non-Lipschitz Constrained Optimizations

作　　者：徐柳静 彭定涛[1] 王鑫[1] 

机构地区：[1]贵州大学数学与统计学院,贵州贵阳550025

出　　处：《贵州大学学报（自然科学版）》2017年第2期10-13,17,共5页Journal of Guizhou University:Natural Sciences

基　　金：国家自然科学基金项目资助(11401124);贵州大学引进人才科研项目资助(201343)

摘　　要：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.

关 键 词：非Lipschitz 约束优化 稀疏解 最优性条件 

分 类 号：O224[理学—运筹学与控制论]