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Classic Machine Learning
·
Module 1
Optimization Foundations
1
Convexity Conditions: First and Second Order
Verify the convexity of functions using first-order and second-order conditions.
2
Gradient Descent: Derivation and Convergence for Convex Functions
Derive the gradient descent update rule from a first-order Taylor approximation and explain its convergence guarantees for convex objectives.
3
Stochastic vs. Batch Gradient Descent: Convergence Analysis
Derive stochastic gradient descent and compare its convergence properties with batch gradient descent.
4
Newton's Method: Optimization and Convergence
Derive Newton's method for optimization and compare its quadratic convergence rate with the linear convergence of gradient descent.
Lagrangian Multipliers and KKT Conditions
Formulate constrained optimization problems using Lagrangian multipliers and derive the Karush-Kuhn-Tucker (KKT) conditions.
6
Lagrangian Duality: Derivation and Strong Duality Conditions
Explain Lagrangian duality, derive the dual problem, and state conditions for strong duality.
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