AM 221: Advanced Optimization


Instructor: Yaron Singer
Time: M./W. 10-11:30 am
Room: Maxwell Dworkin 123
Email:yaron at seas dot harvard dot edu

Staff: We're fortunate to have Karthik Chandrasekaran (karthe at seas dot harvard dot edu), Thibaut Horel (thorel at seas dot harvard dot edu), and Muxi li (muxili at fas dot harvard dot edu) as members of our staff this semester.

Overview: This is a graduate-level course on optimization. The course covers mathematical programming and combinatorial optimization from the perspective of convex optimization, which is a central tool for solving large-scale problems. In recent years convex optimization has had a profound impact on statistical machine learning, data analysis, mathematical finance, signal processing, control, approximation algorithms, as well as many other areas. The first part will be dedicated the theory of convex optimization and its direct applications. The second part will focus on advanced techniques in combinatorial optimization using machinery developed in the first part.

Prerequisites: This will be a mathematically rigorous course. Basic knowledge in linear algebra and competency with calculus are required. AM 121 is certainly helpful but is not a necessary prerequisite. An appreciation for aesthetics, as well as prior coursework in algorithms, machine learning, and statistics will be helpful but not necessary. There will be some simple programming exercises. The course is intended for graduate students, but advanced undergraduates are encouraged to attend as well.

Goals: The goal of this course is to provide strong foundations for students interested in the manipulation of data, broadly defined. In particular, this course is highly recommended for students who are interested in machine learning, algorithms, data-mining, mathematical finance, and microeconomics.

Assessment: The main component of this course will be a research project. This project can be data-oriented or theoretically-focused, or (better) a combination of both. There is room for projects involving algorithms, data mining, machine learning, game theory and mechanism design, and statistics.