基于Lasserre松弛的紧约束多项式优化问题逼近界分析  

APPROXIMATION BOUND ANALYSIS BASED ON THE TIGHT CONSTRAINTS POLYNOMIAL OPTIMIZATION PROBLEMS OF LASSERRE RELAXATION

作　　者：高雷阜[1] 周庆 

机构地区：[1]辽宁工程技术大学优化与决策研究所,辽宁阜新123000

出　　处：《数学杂志》2018年第2期375-380,共6页Journal of Mathematics

基　　金：教育部高校博士学科科研基金联合资助(20132121110009);辽宁省教育厅项目(L2015208)

摘　　要：本文研究了紧约束多项式优化问题(POP)的界.利用Lasserre提出的将原紧约束问题转化为多项式平方和(SOS)成立的条件,给出其条件推导SOS式子成立的证明.利用原有逼近界定理,将其进一步转化,获得了新的逼近界定理.新的逼近界定理较原有定理减少了参数,便于计算.In this paper, the boundary of the tight constraints polynomial optimization problems （POP） is studied. The original tight constraints are transformed into sum of squares （SOS） by Lasserre, and its founded conditions are given. We prove that the founded conditions make the SOS feasible. By using the original approximation bound theorem, the new approxi- mation bound theorem is obtained, and the new approximation bound theorem is reduced by the original theorem, which is easy to calculate.

关 键 词：紧约束 多项式优化问题 多项式平方和 逼近界 

分 类 号：O224[理学—运筹学与控制论]