Approximate GCDs of polynomials and sparse SOS relaxations

Authors:
Bin Li;Jiawang Nie;Lihong Zhi
Affiliations:
Key Lab of Mathematics Mechanization, AMSS, Beijing 100190, China;Department of Mathematics, UCSD, La Jolla, CA 92093, USA;Key Lab of Mathematics Mechanization, AMSS, Beijing 100190, China
Venue:
Theoretical Computer Science
Year:
2008

Citing 16
Cited 0

Semidefinite programming

SIAM Review
Approximate polynomial greatest common divisors and nearest singular polynomials

ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Optimization strategies for the approximate GCD problem

ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On approximate GCDs of univariate polynomials

Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Nearest singular polynomials

Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Efficient algorithms for computing the nearest polynomial with a real root and related problems

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Global Optimization with Polynomials and the Problem of Moments

SIAM Journal on Optimization
Sparsity in sums of squares of polynomials

Mathematical Programming: Series A and B
Global optimization of rational functions: a semidefinite programming approach

Mathematical Programming: Series A and B
Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

SIAM Journal on Optimization
Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials

Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Convergent SDP-Relaxations in Polynomial Optimization with Sparsity

SIAM Journal on Optimization
Global minimization of rational functions and the nearest GCDs

Journal of Global Optimization
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Sparse SOS Relaxations for Minimizing Functions that are Summations of Small Polynomials

SIAM Journal on Optimization

Quantified Score

Hi-index	5.23

Visualization

Abstract

The problem of computing approximate GCDs of several polynomials with real or complex coefficients can be formulated as computing the minimal perturbation such that the perturbed polynomials have an exact GCD of given degree. We present algorithms based on SOS (Sums Of Squares) relaxations for solving the involved polynomial or rational function optimization problems with or without constraints.