Lower bound functions for polynomials

Authors:
Jürgen Garloff;Christian Jansson;Andrew P. Smith
Affiliations:
Department of Computer Science, University of Applied Sciences/FH Konstanz, Postfach, 100543, D-78405 Konstanz, Germany;Technical University Hamburg-Harburg, Institute of Computer Science III, Schwarzenbergstr. 95, D-21071 Hamburg, Germany;University of Applied Sciences/FH Konstanz, Institute for Applied Research, Postfach 100543, D-78405 Konstanz, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

Citing 9
Cited 8

Discrete optimization

Discrete optimization
New computer methods for global optimization

New computer methods for global optimization
A collection of test problems for constrained global optimization algorithms

A collection of test problems for constrained global optimization algorithms
Error estimates for approximations from control nets

Computer Aided Geometric Design
Box-bisection for solving second-degree systems and the problem of clustering

ACM Transactions on Mathematical Software (TOMS)
Curves and surfaces for CAGD: a practical guide

Curves and surfaces for CAGD: a practical guide
Convergent Bounds for the Range of Multivariate Polynomials

Proceedings of the International Symposium on Interval Mathemantics 1985
Inclusion isotonicity of convex-concave extensions for polynomials based on Bernstein expansion

Computing
Optimized refinable enclosures of multivariate polynomial pieces

Computer Aided Geometric Design

Inclusion isotonicity of convex-concave extensions for polynomials based on Bernstein expansion

Computing
Fast construction of constant bound functions for sparse polynomials

Journal of Global Optimization
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion

CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
An efficient algorithm for range computation of polynomials using the Bernstein form

Journal of Global Optimization
Enhancing numerical constraint propagation using multiple inclusion representations

Annals of Mathematics and Artificial Intelligence
Polytope-based computation of polynomial ranges

Computer Aided Geometric Design
A comparison of methods for the computation of affine lower bound functions for polynomials

COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
The Bernstein polynomial basis: A centennial retrospective

Computer Aided Geometric Design

Quantified Score

Hi-index	7.29

Visualization

Abstract

Relaxation techniques for solving nonlinear systems and global optimisation problems require bounding from below the nonconvexities that occur in the constraints or in the objective function by affine or convex functions. In this paper we consider such lower bound functions in the case of problems involving multivariate polynomials. They are constructed by using Bernstein expansion. An error bound exhibiting quadratic convergence in the univariate case and some numerical examples are given.