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The Trouble with Quadratic Penalties: ALM as a Fix
This lecture delves into the challenges posed by quadratic penalties in optimization problems, exploring the use of Augmented Lagrangian Methods (ALM) as a solution. The instructor discusses the properties of quadratic penalties, theorems related to penalty weights, and the application of ALM to handle infeasibility. The lecture also covers the Augmented Lagrangian method for equality constraints, providing a detailed algorithm and theoretical background. Through examples and detailed explanations, the lecture aims to elucidate the intricacies of using ALM to address optimization problems with quadratic penalties.