Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Add branch-and bound algorithm to bound polynomials #32

Open
lbenet opened this issue Feb 20, 2019 · 3 comments
Open

Add branch-and bound algorithm to bound polynomials #32

lbenet opened this issue Feb 20, 2019 · 3 comments

Comments

@lbenet
Copy link
Member

lbenet commented Feb 20, 2019

The idea is to have other methods to improve bounding polynomials, specially with many variables.

@mforets
Copy link
Contributor

mforets commented Feb 20, 2019

For a pseudo-code implementing branch-and-bound to bound polynomials see e.g. Algorithm 1 in Implementation of Taylor Models in CORA 2018. M. Althoff, D. Grebenyuk and N. Kochdumper.

@lbenet
Copy link
Member Author

lbenet commented Feb 20, 2019

For a pseudo-code implementing branch-and-bound to bound polynomials see e.g. Algorithm 1 in Implementation of Taylor Models in CORA 2018. M. Althoff, D. Grebenyuk and N. Kochdumper.

@dpsanders has a bunch of experience on this. I am thinking of IntervalRootFinding.jl, but perhaps IntervalOptimization.jl is another good option.

In the past I used the function bound_taylor1 (already in TaylorModels.jl) to achieve tighter bounds, but since then IntervalRootFinding.jl has changed a bit, and the methods I introduced are certainly out of date.

@dpsanders
Copy link
Member

This is what is implemented in IntervalOptimization.jl, although there will be some details to sort out to make it workable for e.g. > 2 variables. Also, at the moment it is difficult to make it stop in particular circumstances.

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

No branches or pull requests

3 participants