Concept

Convex polytope

Related lectures (32)

Explores Hamiltonian dynamics on convex polytopes, covering symplectic capacities, EHZ capacity, and systolic ratio maximizers.

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

Explores convex polyhedra, linear programs, and their optimization importance.

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

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

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

Explores the Brunn-Minkowski inequality in convex geometry and related concepts.

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

Covers geodesically convex optimization on Riemannian manifolds, exploring convexity properties and minimization relationships.

Explores optimization on convex sets, including KKT points and tangent cones.

Explores the closest vector problem in lattices and the role of Voronoi cells in determining the closest vector.

Demonstrates the process of including beams and correcting orientations for complex configurations.

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

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

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

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

Covers line metrics, convex cones, and linear metric combinations.

Explores the characteristics of parabolic conicity and demonstrates how to address related issues.

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

Covers the Branch and Bound algorithm, focusing on formal description and implementation steps to find optimal integer solutions.