利用统一框架设计凸优化的分裂收缩算法  

USING A UNIFIED FRAMEWORK TO DESIGN THE SPLITTING AND CONTRACTION METHODS FOR CONVEX OPTIMIZATION

作　　者：何炳生[1] He Bingsheng(Department of Mathematics,Nanjing University,Nanjing 210093)

机构地区：[1]南京大学数学系,南京210093

出　　处：《高等学校计算数学学报》2022年第1期1-35,共35页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金委NSFC Grant 11871029资助项目。

摘　　要：1引言应用领域内提出的大量优化问题中,包含了许多可以归结为(或者松弛成)如下典型的线性约束凸优化问题:1.线性约束的单块凸优化问题min{θ(x)|Ax=b(or≥b),x∈χ}.2.线性等式约束的可分离成两块的凸优化问题。In order to solve the linearly constrained convex optimization problems,by using the concepts of variational inequality(VI) and proximal point algorithm(PPA),we have gradually summed up and developed a simple and powerful algorithmic unified framework.By verifying the conditions in this framework,the convergence proofs of many existing algorithms becomes very simple.Based on this framework,we can construct the appropriate algorithms for different problems.Under the guidance of the framework,this paper presents some algorithms which widely expand the classical algorithms of the ALM and/or ADMM-like classes.

关 键 词：线性等式约束 凸优化问题 线性约束 框架设计 应用领域 收缩算法 

分 类 号：O221.2[理学—运筹学与控制论] O224[理学—数学]