求解非线性二阶锥规划的Carroll函数方法的收敛性分析（英文）  

Convergence Analysis of Carroll Function Method for Nonlinear SOC Programs

作　　者：顾剑[1] 肖现涛[2] 

机构地区：[1]大连海洋大学理学院,辽宁大连116024 [2]大连理工大学数学科学学院,辽宁大连116023

出　　处：《应用数学》2016年第4期855-870,共16页Mathematica Applicata

基　　金：Supported by the Ph.D.Programs Foundation of the Ministry of Education of China(20110041120039)

摘　　要：本文构造了求解非线性规划问题的基于Carroll函数的非线性拉格朗日方法.在严格互补条件、约束非退化条件和二阶充分条件成立的前提下,本文证明了Carroll非线性拉格朗日方法的收敛性.在上述条件下,当罚参数小于某常数并且最优解的误差界和罚参数成某比例时,分析该算法的局部收敛速度.最后,给出一些初步的数值实验结果.This paper focuses on the study of the rate of convergence for the nonlinear Lagrangian method based on Carroll function for nonconvex nonlinear second-order cone programming. A set of conditions, including the componentwise strict complementarity condition, the constraint nondegeneracy condition and the second order sufficient condition, are used to guarantee the convergence of Carroll function method. The convergence theorem shows that under above conditions the dual algorithm based on Carroll function is locally convergent when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Moreover, numerical results are reported to show the efficiency of the proposed method.

关 键 词：Carroll函数 非线性二阶锥规划 非线性拉格朗日方法 收敛性分析 

分 类 号：O221.2[理学—运筹学与控制论]