Abstract

This paper presents a branch & cut algorithm to find all isolated solutions of a system of polynomial constraints. Our findings show that fairly straightforward refinements of interval methods inspired by AI constraint propagation techniques result in a multivariate root finding algorithm that is competitive with continuation methods on most benchmarks and which can solve a variety of systems that are totally infeasible for continuation methods. For example, we can solve the Broyden Banded function benchmark for hundreds of variables and hundreds of cubic equations. 1 Introduction In this paper we consider the classical problem of finding solutions to systems of nonlinear polynomial equations in many variables. This is an old problem with many applications and a large literature. In engineering applications it is generally sufficient to find an assignment of floating point numbers to variables such that the given constraints are satisfied to within the uncertainty introduced by the q...

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