Convex Optimization: Self-dual Cones

This lecture covers the concept of self-dual cones in convex optimization, where the dual cone is defined as the set of vectors that satisfy certain conditions. It explains how specific cones, such as the non-negative orthant and positive semidefinite cone, are their own duals. The lecture also delves into various optimization problems, including SDPs, congruence transformations, and mechanical equilibrium, showcasing their convexity and duality properties.