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Majorization-Minimization Procedures and Multi-Objective Optimization

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Technical Report,15 Sep 2015,14 Sep 2018

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Fondat J J Laffont Tlse Sciences Eco Toulouse France

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This project revolved around so-called majorization-minimization methods in optimization. These types of methods are of particular importance in machine learning and statistics and applicable to a wide range of Air Force applications. In particular, Jerome established rigorous convergence results and convergence rates for a variety of non-convex problems encountered in image and phase retrieval problems. Such theoretical results guide and underpin the engineering application of these algorithms. In all, this project produced 12 journal articles, many in top journals 2 in Mathematical Programming and 2 in SIAM Optimization. Most notably, during the second year of the project, Jrme Bolte was awarded the SIAM Optimization prize with S. Sabach and M. Teboulle, for the paper Proximal Alternating Linearized Minimization for Nonconvex and Nonsmooth Problems. Jerome will be continuing similar work with a follow-on AFOSR grant. A full list of papers and results can be found in the attached report.

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  • Operations Research

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