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Explore model-based optimization with convex-composite optimization in this comprehensive lecture by Jim V. Burke, presented at the Colloque des sciences mathématiques du Québec (CSMQ). Delve into the balance between model complexity and computational tractability, while examining techniques for post-optimal analysis and stability measures. Discover the convex-composite modeling framework, which encompasses a wide range of optimization problems, including nonlinear programming, feasibility, minimax optimization, sparsity optimization, feature selection, Kalman smoothing, parameter selection, and nonlinear maximum likelihood. Learn how to identify and exploit underlying convexity in problems to leverage rich theoretical foundations and efficient numerical methods. Trace the development of convex-composite problems from the 1970s to their recent resurgence, driven by emerging methods in approximation, regularization, and smoothing. Understand the relevance of these techniques to global health, environmental modeling, image segmentation, dynamical systems, signal processing, machine learning, and AI. Review the convex-composite problem structure, variational properties, and algorithm design, with potential insights into applications for signal processing filtering methods.
