Sum of squares methods for minimizing polynomial forms over spheres and hypersurfaces

DOI10.1007/s11464-012-0187-4zbMath1277.65046OpenAlexW2116854630MaRDI QIDQ693193

Jia-Wang Nie

Publication date: 7 December 2012

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-012-0187-4

zbMATH Keywords

algorithmsemidefinite programminghypersurfacepolynomial\(L^2\)-normunit sphereNP-hard problemapproximation bound\(G\)-normmulti-formmulti-unit spheresum of squares relaxation

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Semidefinite programming (90C22) Approximation methods and heuristics in mathematical programming (90C59)

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Extremal cubics on the circle and the 2-sphere ⋮ Certifying the global optimality of quartic minimization over the sphere ⋮ Unnamed Item ⋮ Rational Generalized Nash Equilibrium Problems ⋮ Generalized truncated moment problems with unbounded sets ⋮ Cross-Hill: a heuristic method for global optimization ⋮ Norm bounds and underestimators for unconstrained polynomial integer minimization ⋮ Approximation algorithms for nonnegative polynomial optimization problems over unit spheres ⋮ Lower bounds for cubic optimization over the sphere ⋮ Best Nonnegative Rank-One Approximations of Tensors ⋮ Symmetric rank-1 approximation of symmetric high-order tensors ⋮ Semi-definite representations for sets of cubics on the two-dimensional sphere

Cites Work

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• Forms derived from the arithmetic-geometric inequality
• Semidefinite programming relaxations for semialgebraic problems
• Sparsity in sums of squares of polynomials
• There are significantly more nonnegative polynomials than sums of squares
• Global Optimization with Polynomials and the Problem of Moments
• Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
• Sparse SOS Relaxations for Minimizing Functions that are Summations of Small Polynomials
• Handbook of semidefinite programming. Theory, algorithms, and applications

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