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First Order Algorithms for Large Scale Convex Optimization

A wide variety of fundamental scientific/engineering applications typically give rise to large scale convex optimization problems leading to challenging difficulties for their solutions and often precluding the use of sophisticated polynomial time methods. Elementary first order methods then remain our best alternative to tackle such problems. This talk reviews some recent advances and results in the design and analysis of gradient-based methods for a broad class of structured smooth and nonmsooth convex minimization problems. We focus on some of the mathematical elements and key ideas underlying the building of first order algorithms, and derive schemes with improved iteration complexity bounds. Throughout the talk, this will be illustrated on a variety of generic models e.g., conic, saddle point and eigenvalue problems, as well as signal recovery problems, e.g., total variation minimization and sensors location.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46