Edouard Pauwels est Professeur à la Toulouse School of Economics.
Titre : Curiosities and counterexamples in smooth convex optimization
Résumé : The presentation is taken from a list of counterexamples to conjectures in smooth convex coercive optimization. We will focus on the gradient descent method with exact line search, and show that the resulting sequence is non convergent in general. This example is based on general smooth convex interpolation results. Given a decreasing sequence of convex compact sets in the plane, whose boundaries are positively curved Ck curves (k > 1, arbitrary), there exists a Ck convex function for which each set from the sequence is a sublevel set. The talk will provide proof arguments for this results and detail how it can be used to construct pathological convex functions. We will conclude with an outline of the list counterexamples following from our smooth interpolation result.