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On a first-order primal-dual algorithm with applications to convex problems in computer vision

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In the first part of the talk I give new results for a first-order primal-dual algorithm to solve non-smooth convex optimization problems with known saddle-point structure. I show that the algorithm converges to a saddle-point with rate O(1/N) for the complete class of problems. Furthermore, I show that we can get better convergence rates on problems with more regularity.

In the second part of the talk, I discuss new preconditioning techniques for the algorithm. In particular, I propose a family of simple and easy to compute diagonal preconditioners for which convergence of the algorithm is guaranteed without the need to compute any step size parameters.

In the third part of the talk I demonstrate the improved performance of the algorithm by applying it to standard linear programming test problems and a few standard computer vision problems such as image restoration, graph cuts, multi-label image segmentation and optical flow.

(Joint work with Antonin Chambolle, CMAP , Ecole Polytechnique)

This talk is part of the Microsoft Research Machine Learning and Perception Seminars series.

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