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This lecture covers Optimization for Machine Learning, focusing on Newton's and Quasi-Newton Methods. It explains the 1-dimensional case of Newton-Raphson method, the Babylonian method for computing square roots, and the secant method. The lecture delves into the convergence of Newton's method, the secant condition, and Quasi-Newton methods. It discusses the downsides of Newton's method, the secant condition, and the development of Quasi-Newton methods. The lecture also touches on strong convexity, bounded inverse Hessians, and the super-exponential convergence of Newton's method. Additionally, it explores the affine invariance of Newton's method and the convergence in one step on quadratic functions.
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