Concept

Convex cone

Related lectures (32)

Equality and Inequality Constraints: Optimization Conditions

Covers necessary optimality conditions for optimization with constraints and discusses cones and polar sets.

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

The polar of the cone of linearized directions

Covers the concept of the polar of the cone of linearized directions and its special cases.

Farkas' Lemma: Applications in Game Theory

Explores Farkas' Lemma, hyperplane separation, combinatorics, and its application in game theory, focusing on penalty kick strategies.

Convex Functions: Theory and Applications

Introduces convex functions, covering affine, convex, and conic hulls, transformations, inequalities, and conditions for convexity.

Convex Sets: MGT-418 Lecture

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

Convex Functions: Elementary Concepts

Introduces elementary concepts of convex functions, including hulls, transformations, conditions, and examples.

Raytracing Intersection Triangle

Explores ray-triangle intersection, barycentric coordinates, points vs. vectors, and other primitives.

Intrinsic Geometry of Regular Surfaces

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Metrics: Line and Convex Cone

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

Semi-Definite Programming

Covers semi-definite programming and optimization over positive semidefinite cones.

Two Inequalities and Feasible Cone: Linearized Approach

Explains feasible directions, linearized cone, and Constraint Qualification conditions in optimization.

Cones of convex sets

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

Kernel Ridge Regression: Equivalent Formulations and Representer Theorem

Explores Kernel Ridge Regression, equivalent formulations, Representer Theorem, Kernel trick, and predicting with kernels.

Closed Surfaces and Integrals

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

Center of Mass: Hollow Cone Inertias

Covers center of mass in hollow cones with negative mass and direct methods.

Convex Optimization

Covers an overview of convex optimization, affine sets, polyhedra, ellipsoids, and convex functions.

Lagrangian Duality: Theory and Applications

Explores Lagrangian duality in convex optimization, discussing strong duality, dual solutions, and practical applications in second-order cone programs.

Projected Gradient Descent

Explores convex constrained optimization through Projected Gradient Descent, focusing on tangent space and iterative minimization.