Chapter 3 Polynomial Optimization

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


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 \(g_i \in \mathbb{R}[x], i=1,\ldots,m\).


Feasible Solution Global Minimizer Cholesky Factor Linear Relaxation Sparsity Pattern 
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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

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