Computing and Optimization

Fall 2024, Princeton University (undergraduate course)

(This is the Fall 2024 version of this course. For the current version, click here. You can also access the Fall 2023, Fall 2021, Fall 2020 ,  Fall 2019,  Fall 2018,  Fall 2017, Fall 2016, Fall 2015, Fall 2014 versions.)

Useful links

• The course syllabus
• Canvas (for Q&A, sign up to Ed Discussion via Canvas)
• Download MATLAB
• MATLAB Tutorial
• Download CVX (or CVXPY if you are a Python user)
• Acknowledgments

Lectures

The notes below summarize most of what I cover during lecture. 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]
   
• 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 Demo
  [cvx_examples.m] (MATLAB), [cvxpy_examples.ipynb] (Python)
   
• 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] 
  Additional slides on applications of sum of squares optimization (optional): [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 Canvas.

• Homework 1: Optimizing Cub Club, perfect numbers, and a review of linear algebra and multivariate calculus.
  [pdf]
   
• Homework 2: Image compression and honoring Sydney McLaughlin, local and global minima, positive semidefinite matrices, copositive matrices.
  [pdf], [mclaughlin.jpg]
   
• Homework 3: Radiation treatment planning, GPA at Yale vs. Princeton, convex analysis.
  [pdf]
  MATLAB specific data files: [treatment_planning_data.m]
  Python specific data files: [treatment_planning_data.py], [Atumor.csv], [Aother.csv] 
   
• Practice Midterms:
  [Fall18], [Fall19], [Fall20], [Fall21], [Fall23]
   
• Midterm:
  [pdf]
   
• Homework 4: Support vector machines, predicting the outcome of an election.
  [pdf], [HWSVM], [Hillary_vs_Bernie]
   
• Homework 5: Theory-application split in a course, approximating the square root, Newton fractals, orbit of the Earth and daily temperature in NYC.
  [pdf], [TemperatureNewYork.csv]
   
• Homework 6:  New gym for Princeton, Lyapunov functions.
  [pdf], [princetoncampus.jpeg], [Circledraw.m], [plotgrid.m], [plotgrid.py]
   
• Homework 7: Setting the odds in your favor with SDP, optimal control, nearest correlation matrix.
  [pdf]
   
• Homework 8: End-of-semester party at AAA’s, Doodle and scheduling, SDP relaxations for nonconvex polynomial optimization, NP-completeness.
  [pdf], [Party_people_in_the_house_tonight.mat], [Doodle_matrix.mat]
   
• Practice Final Exams (data files on Canvas):
   [Fall17], [Fall18], [Fall19], [Fall20], [Fall21], [Fall23]
   
• Final Exam:
  [pdf]