Computing and Optimization Fall 2018, Princeton University (undergraduate course)
Useful links - Blackboard
- Piazza (used only for Q&A - you should sign in to Piazza via Blackboard)
- Download MATLAB
- Download CVX
- The course syllabus (includes times/locations of office hours)
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 Gauss-Newton 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: Limits of computation + course recap.
[pdf]
Problem sets and exams
Solutions are posted on Blackboard.
- Homework 1: Optimize for happiness, perfect numbers, and a review of linear algebra, multivariate calculus, and MATLAB.
[pdf]
- Homework 2: Image compression and SVD, local and global minima, positive semidefinite matrices, copositive matrices and convex sets.
[pdf], [turing.jpg]
- Homework 3: Radiation treatment planning, regression with different penalties, convex sets and functions, optimality conditions.
[pdf], [treatment_planning_data.m]
- Practice Midterm
[pdf],
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