Yves Lucet – Optimization Online

What Shape is your Conjugate? A Survey of Computational Convex Analysis and its Applications

Published: 2007/12/28, Updated: 2009/05/18

Applications - OR and Management Sciences, Convex Optimization computational convex analysis, convex envelope, fast algorithms, legendre-fenchel transform, mathematical morphology, max-plus algebra, partial differential equations

Computational Convex Analysis algorithms have been rediscovered several times in the past by researchers from different fields. To further communications between practitioners, we review the field of Computational Convex Analysis, which focuses on the numerical computation of fundamental transforms arising from convex analysis. Current models use symbolic, numeric, and hybrid symbolic-numeric algorithms. Our objective is … Read more

Fast Moreau Envelope Computation I: Numerical Algorithms

Published: 2005/10/05, Updated: 2007/01/08

Yves Lucet

Convex Optimization, Nonsmooth Optimization, Problem Solving Environments conjugate, discrete legendre transform, envelope of functions, legendre-fenchel transform, linear-time worst-case complexity, moreau-yosida approximate, numerical algorithm

The present article summarizes the state of the art algorithms to compute the discrete Moreau envelope, and presents a new linear-time algorithm, named NEP for NonExpansive Proximal mapping. Numerical comparisons between the NEP and two existing algorithms: The Linear-time Legendre Transform (LLT) and the Parabolic Envelope (PE) algorithms are performed. Worst-case time complexity, convergence results, … Read more