Convexifying Nonconvex Problems: SVM and Dimensionality Reduction
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Introduces linear programming basics, including optimization problems, cost functions, simplex algorithm, geometry of linear programs, extreme points, and degeneracy.
Covers gradient descent methods for convex and nonconvex problems, including smooth unconstrained convex minimization, maximum likelihood estimation, and examples like ridge regression and image classification.
Explores convex optimization, convex functions, and their properties, including strict convexity and strong convexity, as well as different types of convex functions like linear affine functions and norms.
Covers Markov Chain Monte Carlo for sampling high-dimensional distributions, discussing challenges, advantages, and applications like the Knapsack Problem and cryptography.