Work

Minimizing polynomial functions

Year: 2003

Type: book-chapter

Abstract: We compare algorithms for global optimization of polynomial functions in many variables. It is demonstrated that existing algebraic methods (Gröbner bases, resultants, homotopy methods) are dramatically outperformed by a relaxation technique, due to N.Z. Shor and the first author, which involves sums of squares and semidefinite programming. This opens up the possibility of using semidefinite programming relaxations arising from the Positivstellensatz for a wide range of computational problems in real algebraic geometry. This paper was presented at the Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, held at DIMACS, Rutgers University, March 12-16, 2001.

Source: DIMACS series in discrete mathematics and theoretical computer science

DOI: 10.1090/dimacs/060/08

Authors: Pablo Parrilo, Bernd Sturmfels

Institutions: California Institute of Technology, Georgia Institute of Technology, University of California, Berkeley, Universidad de Cantabria

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley

Award: Combinatorial Algebraic Geometry