Lectures related to Convex Functions

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Mathematics of Data: Optimization Basics

Covers optimization basics, including metrics, norms, convexity, gradients, and logistic regression, with a focus on strong convexity and convergence rates.

Gradient Descent Methods: Theory and Computation

Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.

Information Theory: Channel Capacity and Convex Functions

Explores channel capacity and convex functions in information theory, emphasizing the importance of convexity.

Optimization Basics: Norms, Convexity, Differentiability

Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.

Optimization Techniques: Convexity in Machine Learning

Covers optimization techniques in machine learning, focusing on convexity and its implications for efficient problem-solving.

Primal-dual Optimization: Extra-Gradient Method

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

Primal-dual Optimization III: Lagrangian Gradient Methods

Explores primal-dual optimization methods, emphasizing Lagrangian gradient techniques and their applications in data optimization.

Proximal Operators and Constrained Optimization

Introduces proximal operators, gradient methods, and constrained optimization, exploring their convergence and practical applications.

Adversarial Machine Learning: Fundamentals and Techniques

Explores adversarial machine learning, covering the generation of adversarial examples, robustness challenges, and techniques like Fast Gradient Sign Method.

Proximal and Subgradient Descent: Optimization Techniques

Discusses proximal and subgradient descent methods for optimization in machine learning.

Stochastic Gradient Descent: Optimization and Convergence

Explores stochastic gradient descent, covering convergence rates, acceleration, and practical applications in optimization problems.

Convex Optimization: Convex Functions Log in to Mediaspace to watch this video

Covers the concept of convex functions and their applications in optimization problems.

Optimal Transport: Rockafellar Theorem Log in to Mediaspace to watch this video

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Geodesic Convexity: Theory and Applications Log in to Mediaspace to watch this video

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Convex Sets: Theory and Applications Log in to Mediaspace to watch this video

Explores convex sets, their properties, and applications in optimization.

Convex Functions Log in to Mediaspace to watch this video

Covers the properties and operations of convex functions.

Convex Optimization: Gradient Descent Log in to Mediaspace to watch this video

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Optimization Programs: Piecewise Linear Cost Functions Log in to Mediaspace to watch this video

Covers the formulation of optimization programs for minimizing piecewise linear cost functions.

KKT and Convex Optimization Log in to Mediaspace to watch this video

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.