Mathematics of Data: Optimization Basics

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Related lectures (29)

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Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Gradient Descent Methods

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.

Convex Functions

Covers the definition of convex functions and their properties in optimization.

Convexity and Jacobians

Explores convexity, Jacobians, subdifferentials, and convergence rates in optimization and function analysis.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Linear Models: Continued

Explores linear models, regression, multi-output prediction, classification, non-linearity, and gradient-based optimization.

Non-Convex Optimization: Techniques and Applications

Covers non-convex optimization techniques and their applications in machine learning.

Fenchel Conjugation: Basics and Applications

Introduces Fenchel conjugation, exploring its properties, examples, and applications in nonsmooth optimization problems and minimax formulations.