非线性二阶锥优化问题的一种增广Lagrange算法的收敛性  

Convergence Analysis of a Nonlinear Lagrange Method for Optimization Problems over Nonlinear Second-order Cones

作　　者：郭瑾 贺素香 GUO Jin;HE Suxiang(Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan,Hubei,430070,P.R.China)

机构地区：[1]武汉理工大学理学院数学系

出　　处：《数学进展》2019年第6期739-756,共18页Advances in Mathematics（China）

基　　金：中央高校基本科研业务费资助(No.2018IB016)

摘　　要：基于与不等式约束优化问题的一个势函数相应的L?wner算子,建立了一个求解非线性二阶锥优化问题的增广Lagrange算法.分析了L?wner算子及相应增广Lagrange函数的微分性质,并在一些适当的假设条件下详细证明了增广Lagrange算法的收敛速度.This paper proposes a nonlinear Lagrangian based on a L?wner operator associated with a potential function of the optimization problems with inequality constrains for solving nonlinear second-order cone programming problem.The properties of the operator and the nonlinear Lagrangian are discussed.And the paper analyzes the rate of convergence of the nonlinear Lagrange method under a set of suitable conditions.

关 键 词：势函数 Lowner算子 增广Lagrange方法 非线性二阶锥规划 

分 类 号：O221.2[理学—运筹学与控制论]