Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Are there any references discussing an interval algorithm for the vanilla gradient descent method given a function $f \colon \mathbb{R}^n \to \mathbb{R}$?

Edit: In particular, I am searching for an interval algorithm that bounds the path $\phi\bigl([0,t^*]\bigr)$ where $\phi$ is the solution to the ODE $$ \phi'(t) = -\nabla f\bigl(\phi(t)\bigr), \quad \phi(0)=x_0. $$ There are plenty of interval ODE solvers but that is not sufficient for my purpose. I need more precise control over how big the intervals bounding the solution become and how they step.

share|improve this question
    
Are you asking about a line-search part of a gradient descent method, or something else? Perhaps about interval arithmetic? –  hardmath Mar 16 '12 at 18:51
    
Yes, this algorithm should use interval arithmetic. –  James Rohal Mar 16 '12 at 21:15

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.