EE109 Convex Optimization Syllabus  Spring 2019
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Syllabus
Introduction to optimization: Role of optimization, Convexity, Examples
Review of mathematical analysis and linear algebra
Convex sets and convex functions: Operations that preserve
convexity, Conjugate function, conjugate sets, Separating hyperplane
theorem
Convex optimization problems: Definition and examples, Linear
programming, Quadratic programming, Geometric programming,
Semidefinite programming
Duality theory: Lagrangian dual function, Lagrange dual problem,
weak and strong duality, Interpretation of dual variables, KKT
optimality conditions.
Methods and algorithms: Descent methods, Newton methods,
Subgradient method, Barrier interior point method, Primaldual
interior point methods.
Advanced topics: Firstorder methods, Schur convexity (as time allows)
Assessment
Breakdown:
20% homework
20% midterm exam
25% project
35% final exam
We reserve the right to change these weights based on performance of the
entire class.
The course will have biweekly homework in the first three quarters
of the semester, and a project in the last quarter.
Course project should be carried out individually. If you intend to perform the project in a group of two, special permission from the instructor is needed – a group project is only allowed if the project has a big enough scope, and the group must have no more than 2 students. For the project, each student needs to formulate an optimization problem, analyze the optimal solutions or conditions for optimality, and implement a numerical algorithm to solve the problem. The problem can be students's own research (advisor's consent is required), or can be a reproduction of existing results in other papers; if a reproduction, a new algorithmic aspect or new analysis must be developed. The project involves a proposal in midsemester and a class presentation at the end of semester. More information will be given in the project description.
The final is a 24 or 48 hour takehome exam. The midterm exam format is to
be determined.
Textbook
References (these are optional)
BenTal and Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and
Engineering Applications, MPSSIAM Series on Optimization, 2001.
Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Springer, 2003.
David G. Luenberger, Optimization by Vector Space Methods, Wiley, 1997.
R. Tyrell Rockafellar, Convex Analysis, Princeton University Press., 1996
Prerequisites
