Exploiting structure in sum of squares programs
Exploiting structure in sum of squares programs
复制标题
利用平方和程序中的结构
DOI：
10.1109/cdc.2003.1272305
复制
发表时间：
2003
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
我们提出了一个概述的不同技术可用于开发结构的制定半定方案的基础上的平方和分解的多元多项式。我们确定不同种类的多项式系统，可以成功地利用数值效率的代数性质。我们的研究结果适用于三个主要的情况：稀疏多项式，理想的结构存在于系统中明确的等式约束，结构对称性，以及它们的组合。该技术显着改善的大小和数值调节所得到的SDPs，并使用几个面向控制的应用程序进行说明。
We present an overview of the different techniques available for exploiting structure in the formulation of semidefinite programs based on the sum of squares decomposition of multivariate polynomials. We identify different kinds of algebraic properties of polynomial systems that can be successfully exploited for numerical efficiency. Our results apply to three main cases: sparse polynomials, the ideal structure present in systems with explicit equality constraints, and structural symmetries, as well as combinations thereof. The techniques notably improve the size and numerical conditioning of the resulting SDPs, and are illustrated using several control-oriented applications.