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An approximation bound analysis for Lasserre's relaxation in multivariate polynomial optimization

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Publication:384182
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DOI10.1007/s40305-013-0017-8zbMath1277.90157OpenAlexW2017436952MaRDI QIDQ384182

Jia-Wang Nie

Publication date: 27 November 2013

Published in: Journal of the Operations Research Society of China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40305-013-0017-8


zbMATH Keywords

semidefinite programmingpolynomialssum of squaresapproximation boundLasserre's relaxation


Mathematics Subject Classification ID

Semidefinite programming (90C22) Abstract computational complexity for mathematical programming problems (90C60)


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An effective version of Schmüdgen's Positivstellensatz for the hypercube ⋮ Inhomogeneous polynomial optimization over a convex set: An approximation approach



Cites Work

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  • On the complexity of Putinar's Positivstellensatz
  • Quadratic programming with one negative eigenvalue is NP-hard
  • Semidefinite programming relaxations for semialgebraic problems
  • Estimating \(L^\infty\) norms by \(L^{2k}\) norms for functions on orbits.
  • Minimizing polynomials via sum of squares over the gradient ideal
  • Global Optimization with Polynomials and the Problem of Moments
  • Handbook of semidefinite programming. Theory, algorithms, and applications
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