Description
Let $f$ be a $L^2$ measurable function defined over the $n$-dimensional unit-cube and enjoying a quadratic growth property around all of its local minimizers on that domain. Our objective is to design an algorithm that can compute all local minimizers of $f$.
We work in a computational framework where the function $f$ is given by an evaluation program $\Gamma$. This program takes as input rational points in that domain and returns the value of $f$ in finite precision at these points.
We are considering both the framework where this evaluation program is exact -- if the image of $f$ can be represented with a finite amount of bits -- or noisy -- in that case, we assume that the evaluation function takes an extra parameter $\eta$ and returns an approximation that is $\eta$-close to the true value of $f$".
