Global optimization of continuous functions over compact domains

The purpose of the Globtim package is to compute the set of all local minima of a real continuous function over a rectangular domain in $$ \R^n $$. This is carried out in 3 main steps:

1. The input function $f$ is sampled on a tensorized Chebyshev grid.
2. A polynomial approximant is constructed via a discrete least squares.
3. The polynomial system of Partial derivatives is solved by either homotopy continuation (numerical method) or through exact polynomial system solving (symbolic method).

Project Status

In active development.

Installation

The package is directly available from the Julia REPL.

julia> ]
pkg> add Globtim

The exact examples require Msolve to be installed. The other examples rely on HomotopyContinuation.jl for the resolution of the polynomial system encoding the critical points of the objective function.

Examples

See the description page for this package at Globtim.