Global optimization of polynomials restricted to a smooth variety using sums of squares
… n if and only if, f A can be expressed as a sum of squares of polynomials on the truncated
variety generated by the ideal ⟨MA i ⟩, for 0 ≤ i ≤ d. Hence, we can obtain algebraic
certificates for lower bounds on f ⋆ using semi-definite programs. Some numerical
experiments are given. We also discuss how to decrease the number of … Our approach fits
in the framework of sums of squares decompositions of multivariate polynomials through a
relaxation to semi-definite programming (see Shor (1987); Parrilo (2000); Lasserre (2001…
variety generated by the ideal ⟨MA i ⟩, for 0 ≤ i ≤ d. Hence, we can obtain algebraic
certificates for lower bounds on f ⋆ using semi-definite programs. Some numerical
experiments are given. We also discuss how to decrease the number of … Our approach fits
in the framework of sums of squares decompositions of multivariate polynomials through a
relaxation to semi-definite programming (see Shor (1987); Parrilo (2000); Lasserre (2001…
Motivation and Problem statement. Consider the global constrained optimization problem f⋆:= inf x∈ V∩ R n f (x)
Elsevier
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