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).

In active development.

• fix the tests
• build the documentation
• reduce the dependencies
• return what center is used in the output (for each critical point)
• if the L2-norm is not uniform on every cube, we might choose where to re-run.
• Run the Lotka-Volterra with msolve.

The function run_parameter_sweep should take the p_true, p_center a tolerance as input?

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.

See the description page for this package at Globtim.