183 citations · 706 across the 60 of their papers we have counts for
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GloptiNets: Scalable Non-Convex Optimization with Certificates
Gaspard Beugnot, Julien Mairal, Alessandro Rudi
We present a novel approach to non-convex optimization with certificates, which handles smooth functions on the hypercube or on the torus. Unlike traditional methods that rely on a…
Approximation of optimization problems with constraints through kernel Sum-Of-Squares
Pierre-Cyril Aubin-Frankowski, Alessandro Rudi
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been…
Exponential convergence of sum-of-squares hierarchies for trigonometric polynomials
Francis Bach, Alessandro Rudi
We consider the unconstrained optimization of multivariate trigonometric polynomials by the sum-of-squares hierarchy of lower bounds. We first show a convergence rate of …
Second order conditions to decompose smooth functions as sums of squares
Ulysse Marteau-Ferey, Francis Bach, Alessandro Rudi
We consider the problem of decomposing a regular non-negative function as a sum of squares of functions which preserve some form of regularity. In the same way as decomposing non-n…
Infinite-Dimensional Sums-of-Squares for Optimal Control
Eloïse Berthier, Justin Carpentier, Alessandro Rudi +1
We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamilt…
Finding Global Minima via Kernel Approximations
Alessandro Rudi, Ulysse Marteau-Ferey, Francis Bach
We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precisi…
Globally Convergent Newton Methods for Ill-conditioned Generalized Self-concordant Losses
Ulysse Marteau-Ferey, Francis Bach, Alessandro Rudi
In this paper, we study large-scale convex optimization algorithms based on the Newton method applied to regularized generalized self-concordant losses, which include logistic regr…