Convex Sets and Functions Strict-Convexity and Strong-Convexity

By Mark Schmidt et al

Published on Dec. 21, 2020

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Table of Contents

Convex Sets and Functions
Strict-Convexity and Strong-Convexity
Admin Registration forms
Website/Piazza
Tutorials
Assignment 1 due next Friday
Convex Optimization
Key property of convex optimization problems
De nition of Convex Sets
Examples of Simple Convex Sets
Showing a Set is Convex from Intersections
De nition of Convex Sets
Examples of Simple Convex Sets
Operations that Preserve Convexity
Convexity of SVMs
Positive Semi-De nite, Positive De nite, Generalized Inequality
More Examples of Convex Functions
Convex Sets from Functions
Multivariate Chain Rule
Positive-De nite implies Invertibility
Strictly-Convex Functions
AC0De nition of Strict and Strong Convexity

Summary

Convex Sets and Functions Strict-Convexity and Strong-Convexity is a lecture by Mark Schmidt et al that was published in Winter 2020. The lecture covers topics such as convex optimization, key properties of convex optimization problems, definitions of convex sets, examples of simple convex sets, operations that preserve convexity, convexity of Support Vector Machines (SVMs), positive semi-definite and positive definite matrices, and more. The lecture also discusses strict and strong convexity of functions, multivariate chain rule, invertibility of positive-definite matrices, and the definitions of strictly-convex and strongly-convex functions in the context of C0 functions.