Unconstraint global polynomial optimization via Gradient Ideal

2013/01/22 by Marta Abril Bucero, Bucero, Marta Abril, Bernard Mourrain +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1301.5298

openalex publication_date 2013/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we describe a new method to compute the minimum of a real polynomial function and the ideal defining the points which minimize this polynomial function, assuming that the minimizer ideal is zero-dimensional. Our method is a generalization of Lasserre relaxation method and stops in a finite number of steps. The proposed algorithm combines Border Basis, Moment Matrices and Semidefinite Programming. In the case where the minimum is reached at a finite number of points, it provides a border basis of the minimizer ideal.

Citations

• Semidefinite programming relaxations for semialgebraic problems

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• An experimental approach for global polynomial optimization based on Moments and Semidefinite Programming
• Combining SOS and Moment Relaxations with Branch and Bound to Extract Solutions to Global Polynomial Optimization Problems
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• Global optimization of polynomials using gradient tentacles and sums of squares