Advanced Statistical Computing (STA5029), Fall 2025.

Lecture Material

• [Lecture 1-1] Introduction - Why Convex Optimization?

• [Lecture 1-2] Introduction - Convex Sets and Functions

• [Lecture 2-1] Optimization Problems- Optimization Basics

• [Lecture 2-2] Optimization Problems- Canonical Problem Forms

• [Lecture 3-1] First-order Methods I - Gradient Descent

• [Lecture 3-2] First-order Methods I - Subgradients

• [Lecture 4-1] First-order Methods II - Subgradient Method

• [Lecture 4-2] First-order Methods II - Proximal Gradient Descent (and Acceleration)

• [Lecture 5] First-order Methods III - Stochastic Gradient Descent

• [Lecture 6-1] Optimality and Duality I - Duality in Linear Programs

• [Lecture 6-2] Optimality and Duality I - Duality in General Programs

• [Lecture 7-1] Optimality and Duality II - Karush-Kuhn-Tucker (KKT) Conditions

• [Lecture 7-2] Optimality and Duality II - Duality Uses and Correspondences

• [Lecture 8-1] Second-order Methods I - Newton’s Method

• [Lecture 8-2] Second-order Methods I - Barrier Method

• [Lecture 9-1] Second-order Methods II - Primal-Dual Interior-Point Methods

• [Lecture 9-2] Second-order Methods II - Quasi-Newton Methods