Advertisement

Chapter 3 Polynomial Optimization

  • Roberto Cominetti
  • Francisco Facchinei
  • Jean B. Lasserre
Chapter
Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Abstract

In this chapter, we consider the following polynomial optimization problem: \(f^{\ast} = {\text{min}} \{f(x) : x \in K\}\), where \(f \in \mathbb{R}[x]\) is a real-valued polynomial and \({\rm K}\,\subset \mathbb{R}^{n}\) is the basic semi-algebraic set defined by \(K = \{x \in \mathbb{R}^n : g_i(x) \geq 0, i=1,\ldots,m\}\), with \(g_i \in \mathbb{R}[x], i=1,\ldots,m\).

Keywords

Feasible Solution Global Minimizer Cholesky Factor Linear Relaxation Sparsity Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Roberto Cominetti
    • 1
  • Francisco Facchinei
    • 2
  • Jean B. Lasserre
    • 3
  1. 1.Departamento de Ingeniería IndustrialUniversidad de ChileSantiago de ChileChile
  2. 2.Department of Computer, Control, and Management Engineering Antonio RubertiUniversità di Roma “La Sapienza”RomaItaly
  3. 3.LAAS-CNRSToulouseFrance

Personalised recommendations