From the 1 of 9 linked papers with an AI index.
9 papers
Smooth Quasar-Convex Optimization with Constraints
David MartÃnez-Rubio
The paper develops accelerated first-order algorithms for smooth quasar‑convex functions subject to general convex constraints, introducing an inexact accelerated proximal‑point me…
Neural Sum-of-Squares: Certifying the Nonnegativity of Polynomials with Transformers
Nico Pelleriti, Christoph Spiegel, Shiwei Liu +3
Certifying nonnegativity of polynomials is a well-known NP-hard problem with direct applications spanning non-convex optimization, control, robotics, and beyond. A sufficient condi…
Linear Convergence of the Frank-Wolfe Algorithm over Product Polytopes
Gabriele Iommazzo, David MartÃnez-Rubio, Francisco Criado +2
We study the linear convergence of Frank-Wolfe algorithms over product polytopes. We analyze two condition numbers for the product polytope, namely the \emph{pyramidal width} and t…
Secant Line Search for Frank-Wolfe Algorithms
Deborah Hendrych, Mathieu Besançon, David MartÃnez-Rubio +1
We present a new step-size strategy based on the secant method for Frank-Wolfe algorithms. This strategy, which requires mild assumptions about the function under consideration, ca…
Non-Euclidean High-Order Smooth Convex Optimization
Juan Pablo Contreras, Cristóbal Guzmán, David MartÃnez-Rubio
We develop algorithms for the optimization of convex objectives that have Hölder continuous -th derivatives by using a -th order oracle, for any . Our algorithms w…
Beyond Short Steps in Frank-Wolfe Algorithms
David MartÃnez-Rubio, Sebastian Pokutta
We introduce novel techniques to enhance Frank-Wolfe algorithms by leveraging function smoothness beyond traditional short steps. Our study focuses on Frank-Wolfe algorithms with s…