This is a guest post by Nicolas Boumal, a friend and collaborator from Université catholique de Louvain (Belgium), now at Inria in Paris (France), who develops Manopt: a toolbox for optimization on manifolds.
Optimization on manifolds is about solving problems of the form
where is a nice, known manifold. By “nice”, I mean a smooth, finite-dimensional Riemannian manifold.
Continue reading Optimizing in smooth waters: optimization on manifolds
A paper of mine (together with Katya Scheinberg and Luis Nunes Vicente) was recently awarded the 2013 INFORMS Optimization Society student paper prize and so I decided to use the occasion to restart my blog by writing a post about this work.
This paper, entitled “Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization”, was the basis of my Master Thesis back in 2010. In this post I will try to briefly explain the intuition and ideas behind the results in the paper, the actual paper is available here.
The framework is unconstrained optimization: one wants to minimize a (sufficiently smooth) function over . In many applications, function evaluations are particularly expensive and one has no access to function derivatives (an example of this is if the goal is to optimize a set of parameters and each evaluation requires an expensive simulation). Motivated by these applications we are interested in optimizing without using its derivatives and using as few function evaluations as possible, this is known as Derivative-Free Optimization.
Continue reading Computing sparse quadratic models in DFO