Computing and Optimization Fall 2015, Princeton University (undergraduate course)
(This is the Fall 2015 version of this course. For the most recent version click here.)
Useful links
New: all lecture notes and problems sets of Fall 2015 in one file: [pdf] (currently taken down) 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, Lyapunov functions for proving 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
[pdf]
 Lecture 13: Semidefinite programming + SDP relaxations for nonconvex optimization.
[pdf]
 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: Managing the campaign of Donald Trump, perfect numbers, and a review of linear algebra, multivariate calculus, and MATLAB.
[pdf]
 Homework 2: Image compression and SVD, local and global minima, convex sets.
[pdf], [nash.jpg]
 Homework 3: Convex functions, regression under different penalties, optimality conditions, distance between convex sets.
[pdf]
 Homework 4: Support vector machines (SVMs).
[pdf], [data file]
 Practice Midterm (from Fall 2014)
[pdf]
 Midterm
[pdf]
 Homework 5: Radiation treatment planning, Halloween drama, Newton fractals.
[pdf], [treatment_planning_data.m]  Homework 6: New gym and movie theater for Princeton, your own square root solver, rates of convergence, Leontief economy and conjugate gradients.
[pdf], [Circledraw.m], [plotgrid.m]
 Homework 7: Orbit of the Earth and daily temperature in NYC + optimal control + linear programming.
[pdf],

