Projection onto Convex Sets Definition 5(Projection).The projection x of a given point y onto a convex set is defined as the closest point inside the convex set.Formally, x=IIx[y]A arg minxexllx-yll. Theorem 1 (Pythagoras Theorem).Let C Rd be a convex set,y Rd and x IIxly Then for any zEX we have ly-zl≥Πxy-z Advanced Optimization(Fall 2023) Lecture 2.Convex Optimization Basics 11 Advanced Optimization (Fall 2023) Lecture 2. Convex Optimization Basics 11 Projection onto Convex Sets