(10 novembre 2023/November 10, 2023) Colloque des sciences mathématiques du Québec/CSMQ.
Jim V. Burke: Model based optimization with convex-composite optimization.
Abstract: Optimization problems have an enormous variety and complexity and solving them requires techniques for exploiting their underlying mathematical structure. The modeler needs to balance model complexity with computational tractability as well as viable techniques for post optimal analysis and stability measures.
In this talk we describe the convex-composite modeling framework which covers a broad range of optimization problems including nonlinear programming, feasibility, minimax optimization, sparcity optimization, feature selection, Kalman smoothing, parameter selection, and nonlinear maximum likelihood to name a few. The goal is to identify and exploit the underlying convexity that a given problem may possess since convexity allows one to tap into the very rich theoretical foundation as well as the wide range of highly efficient numerical methods available for convex problems. The systematic study of convex-composite problems began in the 1970s concurrent with the emergence of modern nonsmooth variational analysis. The synergy between these ideas was natural since convex-composite functions are neither convex nor smooth. The recent resurgence in interest for this problem class is due to emerging methods for approximation, regularization and smoothing as well as the relevance to a number of problems in global health, environmental modeling, image segmentation, dynamical systems, signal processing, machine learning, and AI. In this talk we review the convex-composite problem structure and variational properties. We then discuss algorithm design and if time permits, we discuss applications to filtering methods for signal processing
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