Linear constraints, Feasible directions

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On Convex Optimization covers course organization, mathematical optimization problems, solution concepts, and optimization methods.

Convex Sets: Mathematical Optimization

Introduces convex optimization, covering convex sets, solution concepts, and efficient numerical methods in mathematical optimization.

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Convex Sets: Theory and Applications

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

Convex Optimization

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

Convex Optimization: Gradient Descent

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

Linear Programming Basics

Introduces linear programming basics, including optimization problems, cost functions, simplex algorithm, geometry of linear programs, extreme points, and degeneracy.

Convex Optimization: Elementary Results

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Optimal Transport: Rockafellar Theorem

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

Linear Constraints: Polyhedron

Explains linear constraints and the concept of a polyhedron in optimization problems.