Chapter 3: Polynomial Optimization, Sums of Squares, and Applications
Chapter 3: Polynomial Optimization, Sums of Squares, and Applications
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第 3 章：多项式优化、平方和及应用
DOI：
10.1137/1.9781611972290.ch3
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
P. Parrilo
中科院分区：
文献类型：
--
作者：
P. Parrilo
我们开始研究本书的主题之一，即非负多项式、平方和和半定规划之间的关系。本章围绕两个关键思想构建：多项式的平方和分解可以使用半定规划来计算，并且寻找实数多项式系统的不可行性证明是一个凸问题。给定证书度数的上限，可以通过求解平方和程序来找到它们。
We begin the study of one of the main themes of the book, namely, the relationships betweennonnegative polynomials,sums of squares, andsemidefinite programming. The two key ideas around which this chapter is structured aresum of squares decompositions of polynomials can be computed using semidefinite programming,andthe search for infeasibility certificates for real polynomial systems is a convex problem. Given an upper bound on the degree of the certificates, they can be found by solving a sum of squares program.