Concept

Convex analysis

Related lectures (29)

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

Introduces convex optimization, focusing on the importance of convexity in algorithms and optimization problems.

Linear Programming Techniques in Reinforcement Learning

Covers the linear programming approach to reinforcement learning, focusing on its applications and advantages in solving Markov decision processes.

Legendre Transform

Explores the Legendre transform, duality in convex analysis, and optimization problems.

Faster Gradient Descent: Projected Optimization Techniques

Covers faster gradient descent methods and projected gradient descent for constrained optimization in machine learning.

Minkowski-Weyl: Convexity and Separation Theorem

Explores convex sets, Minkowski-Weyl theorem, and Separation theorem in convex analysis.

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.

Conjugate Duality: Envelope Representations and Subgradients

Explores envelope representations, subgradients, and the duality gap in convex optimization.

Support Vector Machines: Maximizing Margin

Explores Support Vector Machines, maximizing margin for robust classification and the transition to soft SVM for non-linearly separable data.

Convex Optimization

Introduces the fundamentals of convex optimization, emphasizing the significance of convex functions in simplifying the minimization process.

Convex Optimization: Epigraphs

Explores epigraphs, convexity of bivariate functions, and log-sum-exp functions in convex optimization.

Optimal Transport: Convex Analysis

Explores optimal transport and convex analysis, emphasizing convex functions and their applications.

Stochastic Gradient Descent: Optimization and Convergence

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

Convex Optimization: Gradient Flow

Explores convex optimization, emphasizing the importance of minimizing functions within a convex set and the significance of continuous processes in studying convergence rates.

Convexity and Jacobians

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

Convex Optimization Tutorial: KKT Conditions

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Structured Sparsity: Atomic Norms and Convex Optimization

Explores atomic norms, convex optimization, and structured sparsity in mathematical data analysis.

From Stochastic Gradient Descent to Non-Smooth Optimization

Covers stochastic optimization, sparsity, and non-smooth minimization via subgradient descent.

KKT and Convex Optimization

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

Conjugate Duality: Understanding Convex Optimization

Explores conjugate duality in convex optimization, covering weak and supporting hyperplanes, subgradients, duality gap, and strong duality conditions.