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Description: The aim of this
course is to introduce the main ideas of optimization
theory together with modern techniques for solving
convex optimization problems. Matlab will be the
scientific programming language for this
course. Assignments may involve a fair amount of
scientific programming in matlab together with more
classical exercises
Prerequisite: - ACM 100(abc),
ACM 104 (Linear algebra), or undergraduate equivalent or
consent of instructor. Some programming experience or
some willingless to learn. Prior knowledge of matlab
not required.
Syllabus:
- Convex sets and convex functions
- Convex optimization: linear programming, quadratic programming, geometric programming
- Duality theory: Lagrange multipliers, KKT
optimality conditions, saddlepoints
- Unconstrained minimization: descent methods, gradient and steepest decent methods, Newton's method
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Constrained minimization: equality constraints, Newton's method with equality constraints
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Interior point methods: inequality constraints, primal-dual interior point methods, logarithmic barrier methods
The course will also develop applications in
statistical estimation and approximation.
Textbooks:
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Convex Optimization by Stephen Boyd and Lieven Vandenberghe, Cambridge
University Press (Required)
- A Mathematical View of Interior-Point Methods in Convex
Optimization (MPS-SIAM Series on Optimization) by James Renegar,
SIAM---MPS-SIAM Series on Optimization (optional)
- Nonlinear Programming by Dimitri P. Bertsekas, Athena Scientific;
2nd edition (optional)
- Numerical Optimization by Jorge Nocedal and Stephen Wright,
Springer Verlag; second edition (optional)
Handouts: I will do my best to
post online all the handouts given in class. Also,
Sheila Shull (217 Firestone) is a person you can contact
at any time (between 9:30am and 5pm) if you need
administrative information. Her phone number is
626-395-4560.
Teaching
Assistant and Office Hours:
Peter
Stobbe, Tuesday 4-5:30 p.m., 226 Guggenheim
stobbe@acm.caltech.edu
Grading:
Homework assignments: 60%
Homework will generally be distributed on Wednesdays and
due in class the following Wednesday.
There will be about 5 assignments, and your
lowest score will be dropped in the final grade.
Late homeworks will NOT be accepted for grading
(medical emergencies excepted with proof).
Final exam: 40%. There will be a
take-home final exam.
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