Optimization Methods

1

Gradients & Descent

Calculus foundations, gradients, Jacobians, level curves, and the gradient descent algorithm.

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2

Convex Sets

Convex combinations, metric spaces, hyperplanes, norm balls, and operations preserving convexity.

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3

Analysis

Foundations of topology: Infimum, Supremum, Open/Closed Sets, Interior, and Boundary.

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4

Convex Functions

Jensen's inequality, First/Second order conditions, Log-Sum-Exp, and Log-Determinant.

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5

Convex Optimization Problems

Standard forms, optimality conditions, and problem transformations.

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6

Duality

Lagrange multipliers, geometric intuition, and the transformation from primal to dual.

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7

Recommender Systems

Matrix factorization, loss functions, and gradient descent for recommendations.

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8

Support Vector Machines

Max-margin classifiers, primal/dual formulations, and the kernel trick.

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