Convergent SDP-relaxations for polynomial optimization with sparsity

Authors:
Jean B. Lasserre
Affiliations:
LAAS-CNRS and Institute of Mathematics, LAAS, Toulouse, France
Venue:
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Year:
2006

Citing 8
Cited 0

Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework

SIAM Journal on Optimization
Global Optimization with Polynomials and the Problem of Moments

SIAM Journal on Optimization
An Explicit Equivalent Positive Semidefinite Program for Nonlinear 0-1 Programs

SIAM Journal on Optimization
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi

ACM Transactions on Mathematical Software (TOMS)
Sparsity in sums of squares of polynomials

Mathematical Programming: Series A and B
Generalized Lagrangian Duals and Sums of Squares Relaxations of Sparse Polynomial Optimization Problems

SIAM Journal on Optimization
Optimization of Polynomials on Compact Semialgebraic Sets

SIAM Journal on Optimization
Convergent SDP-Relaxations in Polynomial Optimization with Sparsity

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider a polynomial programming problem P on a compact basic semi-algebraic set K⊂ℝn, described by m polynomial inequalities gj(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.