Noticias en español
Convexity of the image of quadratic functions: a geometric point of view
Abstract: The convexity of the image of quadratic functions is crucial when stablishing Farkas-type alternative results (known as s-lemmas in the quadratic context), which are relevant in many applications. A geometric point of view is presented, which strongly relies in the graphic properties of the image of simple sets of $\R^n$. This gives new understanding on the problem, simplifies classical results and leads to new ones, explained in this talk.
Read MoreLow distortion embeddings of metric graphs and linear properties of Banach spaces
Abstract: We will survey examples of metric graphs whose low distortion embeddability into a Banach space X implies various linear properties for X such as non-reflexivity, containement of $\ell_1$ or large Szlenk index. In some cases the implications can be reversed (up to a renorming).
Read MoreLipschitz-free spaces
Abstract: Let M be a pointed metric space and Lip0 (M ) the space of Lipschitz functions vanishing at 0. Endowed with the Lipschitz norm this space is a Banach space. Denote F(M ) the closed subspace of Lip(M )* spanned by the evaluation points and call it the Lipschitz-free space over M. After an introduction explaining how one can use these spaces in the context of non linear classification of Banach spaces, we will more particularly be interested in dual Lipschitz-free spaces and shortly explain there link with optimal transportation.
Read MoreRecent advances on the acceleration of first-order methods in convex optimization
Abstract: Let f : H → R ∪ {+∞} be a proper lower-semicontinuous convex function defined on a Hilbert space H (think of RN), and let (xk) be a sequence in H generated by means of a “typical” first-order method, and intended to minimize f. If argmin(f) ̸= ∅, then (xk) will converge weakly, as k → +∞, to a minimizer of f, with a worst-case theoretical convergence rate of f(xk) − min(f) = O(1/k). In the 1980’s Y. Nesterov came up with a revolutionary – yet remarkably simple! – idea to modify the computation of the iterates with essentially the same computational cost, in order to...
Read MoreIncremental Proximal and Augmented Lagrangian Methods for Convex Optimization: A Survey
Abstract: Incremental methods deal effectively with an optimization problem of great importance in machine learning, signal processing, and large-scale and distributed optimization: the minimization of the sum of a large number of convex functions. We survey these methods and we propose incremental aggregated and nonaggregated versions of the proximal algorithm. Under cost function differentiability and strong convexity assumptions, we show linear convergence for a sufficiently small constant stepsize. This result also applies to distributed asynchronous variants of the method, involving...
Read MoreWhat is…the inverse function theorem
Abstract: After a gentle introduction to the paradigm of the inverse function theorem, advanced version of this theorem will be presented for nonsmooth functions and set-valued mappings.
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