The problem of low-rank approximation with convex constraints, which often appears in data analysis, image compression and model order reduction, is considered. Given a data matrix, the objective is to find an approximation of desired lower rank that fulfills the convex constraints and minimizes the distance to the data matrix in the Frobenius-norm. The problem of matrix completion can be seen ...

We study succinct approximation of functions that have noisy oracle access. Namely, construction of a succinct representation of a function, given oracle access to an L-approximation of the function, rather than to the function itself. Specifically, we consider the question of the succinct representation of an approximation of a convex function φ that cannot be accessed directly, but only via o...

We propose a method for minimizing a non-convex function, which can be split up into a sum of simple functions. The key idea of the method is the approximation of the convex envelopes of the simple functions, which leads to a convex approximation of the original function. A solution is obtained by minimizing this convex approximation. Cost functions, which fulfill such a splitting property are ...

In this paper, we study the error in the approximation of a convex function obtained via a one-parameter family of approximation schemes, which we refer to as barycentric approximation schemes. For a given finite set of pairwise distinct points Xn := {xi}ni=0 in R, the barycentric approximation of a convex function f is of the form: