Computing and Optimization Fall 2014, Princeton University (undergraduate course)
(This is the Fall 2014 version of this course. For the most recent version click here.)
Useful links Lectures The lecture notes below summarize most of what I cover on the blackboard during class. Please complement them with your own notes. Some lectures take one class session to cover, some others take two.
 Lecture 1: Let's play two games! (Optimization, P and NP.)
[pdf], [ppt]
 Lecture 2: What you should remember from linear algebra and multivariate calculus.
[pdf]
 Lecture 3: Unconstrained optimization, least squares, optimality conditions.
[pdf]
 Lecture 4: Convex optimization I.
[pdf]
 Lecture 5: Convex optimization II.
[pdf]
 CVX: Basic examples.
[m]
 Lecture 6: Applications in statistics and machine learning: LASSO + Support vector machines (SVMs)
[pdf]
 Lecture 7: Root finding and line search. Bisection, Newton, and secant methods.
[pdf]
 Lecture 8: Gradient descent methods, analysis of steepest descent, convergence and rates of convergence.
[pdf]
 Lecture 9: Multivariate Newton, quadratic convergence, Armijo stepsize rule, nonlinear least squares and the GaussNewton algorithm.
[pdf]
 Lecture 10: Conjugate direction methods, solving linear systems, Leontief economy.
[pdf]
 Lecture 11: Linear programming: applications, geometry, and the simplex algorithm.
[pdf]
 Lecture 12: Duality + robust linear programming
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 Lecture 13: Semidefinite programming + SDP relaxations for nonconvex optimization.
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 Lecture 14: A working knowledge of computational complexity theory for an optimizer.
[pdf]
 Lecture 15: Discrete optimization at IBM Research, William Pierson Field Lecture, Dr. Sanjeeb Dash (IBM Research).
[pdf]
 Lecture 16: Limits of computation + course recap.
[pdf]
Problem sets and exams
Solutions are posted on Blackboard. Exams are also posted on Blackboard.
 Homework 1: Brush up on linear algebra, multivariate calculus, and MATLAB.
[pdf]
 Homework 2: Image compression and SVD, optimality conditions, convex sets.
[pdf], [albert.jpg]
 Homework 3: Convex analysis and convex optimization.
[pdf]
 Homework 4: Support vector machines (SVMs).
[pdf], [data file]
 Homework 5: New gym and movie theater for Princeton + Newton fractals.
[pdf], [Circledraw.m], [plotgrid.m]
 Homework 6: Leontief economy + conjugate gradients + radiation treatment planning.
[pdf], [treatment_planning_data.m]
 Homework 7: Optimal control + linear programming.
[pdf]
 Homework 8: Endofsemester party at AAA's + Doodle and scheduling + SDP relaxations + NPcompleteness.

