The University of Texas at Austin

Computer Science 395T


This course will cover a wide range of topics in numerical optimization. The major goal is to learn a set of tools that will be useful for research in Artificial Intelligence and Computer Graphics. The course is a graduatelevel course that combines instruction of basic material, written homeworks , and a final project. The course material integrates the theory of optimization and concrete real applications. Grading is based on homeworks (50%) and the final project (50%).
Prereqs: The course assumes a good knowledge of linear algebra and probability. Please talk to me or email me if you are unsure if the course is a good match for your background.
Textbook: Numerical Optimization.
Date  Topics  Reading  Notes 
August 31th  Introduction  
September 5th  Linear Algebra and Probability I  Introduction to linear algebra.  Homework 1. 
September 7th  Linear Algebra and Probability II  Basic concentration bounds.  
September 12th  Fundamentals of Unconstrained Optimization  
September 14th  Line Search Methods I (Wolfe Conditions)  
September 19th  Line Search Methods II (Global Convergence)  
September 21th  Trust Region Methods I (Subproblem)  Homework 1 due. Homework 2 out.  
September 26th  Trust Region Methods II (Global Convergence)  
September 28th  Trust Region Methods (Applications)  
October 3th  Conjugate Gradient Methods (Linear)  
October 5th  Conjugate Gradient Methods (Nonlinear)  Homework 2 due. Homework 3 out.  
October 10th  Proximal Gradient Methods  
October 12th  Fundamentals of Constrained Optimization  
October 17th  Linear Programming I (The Simplex Method)  Final project proposal Due.  
October 19th  Linear Programming II ( Penalty, Barrier)  Homework 3 due. Homework 4 out.  
October 24th  Linear Programming III (Augmented Lagrange Methods)  
October 26th  Linear Programming IV (Applications)  
October 31th  Quadratic Programming (Algorithms and Applications)  
November 2nd  Guest Lecture  
November 7th  Semidefinite Programming (Algorithms and Applications)  
November 9th  Spectral Methods I (Theory)  
November 14th  Spectral Methods II (Algorithms)  Homework 4 due. Homework 5 out.  
November 16th  Spectral Methods III (Applications)  
Novmeber 21th  Topics in Convex Optimization I (Compressive Sensing)  
November 28th  Topics in Convex Optimization II (Lowrank Matrix Recovery)  
November 30th  Topics in NonConvex Optimization I (Lowrank Matrix Recovery)  
December 5th  Topics in NonConvex Optimization II (Deep Neural Networks)  Homework 5 due.  
December 7th  Topics in NonConvex Optimization III (Reweighted Least Squares)  Final project report due. 