Convergent SDP-Relaxations for Polynomial Optimization with Sparsity

  • Jean B. Lasserre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4151)


We consider a polynomial programming problem P on a compact basic semi-algebraic set K ⊂ ℝ n , described by m polynomial inequalities g j (X)≥0, and with criterion f ∈ ℝ[X]. We propose a hierarchy of semidefinite relaxations that take sparsity of the original data into account, in the spirit of those of Waki et al. [7]. The novelty with respect to [7] is that we prove convergence to the global optimum of P when the sparsity pattern satisfies a condition often encountered in large size problems of practical applications, and known as the running intersection property in graph theory.


Chordal Graph Sparsity Pattern Matrix Completion Polynomial Optimization Polynomial Optimization Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jean B. Lasserre
    • 1
  1. 1.LAAS-CNRS and Institute of MathematicsLAASToulouseFrance

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