8 papers
A constructive approach to strengthen algebraic descriptions of function and operator classes
Anne Rubbens, Julien M. Hendrickx, Adrien Taylor
It is well known that functions (resp. operators) satisfying a property~ on a subset cannot necessarily be extended to a function (resp. operator) satisf…
Identification of Nonlinear Acyclic Networks in Continuous Time from Nonzero Initial Conditions and Full Excitations
Ramachandran Anantharaman, Renato Vizuete, Julien M. Hendrickx +1
We propose a method to identify nonlinear acyclic networks in continuous time when the dynamics are located on the edges and all the nodes are excited. We show that it is necessary…
Computer-aided analyses of stochastic first-order methods, via interpolation conditions for stochastic optimization
Anne Rubbens, Sébastien Colla, Julien M. Hendrickx
This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given…
On the Convex Interpolation for Linear Operators
Nizar Bousselmi, Zhicheng Deng, Jie Lu +2
The worst-case performance of an optimization method on a problem class can be analyzed using a finite description of the problem class, known as interpolation conditions. In this…
A constraint-based approach to function interpolation, with application to performance estimation for weakly convex optimisation
Anne Rubbens, Julien M. Hendrickx
We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradi…
Numerical Design of Optimized First-Order Algorithms
Yassine Kamri, Julien M. Hendrickx, François Glineur +1
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimatio…