Computing and Optimization

Fall 2021, Princeton University (undergraduate course)

(This is the Fall 2021 version of this course. You can also access the current version, or the 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
• Download CVX
• 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.)
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• Lecture 2: What you should remember from linear algebra and multivariate calculus.
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• Lecture 3: Unconstrained optimization, least squares, optimality conditions.
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• Lecture 4: Convex optimization I.
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• Lecture 5: Convex optimization II.
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• CVX: Basic examples.
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• Lecture 6: Applications in statistics and machine learning: LASSO + Support vector machines (SVMs)
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• Lecture 7: Root finding and line search. Bisection, Newton, and secant methods.
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• Lecture 8: Gradient descent methods, analysis of steepest descent, convergence and rates of convergence, Lyapunov functions for proving convergence.
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• Lecture 9: Multivariate Newton, quadratic convergence, Armijo stepsize rule, nonlinear least squares and the Gauss-Newton algorithm.
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• Lecture 10: Conjugate direction methods, solving linear systems, Leontief economy.
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• Lecture 11: Linear programming: applications, geometry, and the simplex algorithm.
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• 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.
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• Lecture 15: Limits of computation + course recap.
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Problem sets and exams

Solutions are posted on Canvas.

• Homework 1:
• Homework 2:
• Homework 3:
• Homework 4:
• Practice Midterms
• Midterm
• Homework 5:
• Homework 6:
• Homework 7:
• Homework 8:
• Practice Finals
• Final Exam