ORF 363 / COS 323, F21

Computing and Optimization

Fall 2021, Princeton University (undergraduate course)

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

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