CS599: Convex and Combinatorial Optimization (Fall 2013)

Basic information


Schedule by Week

Course Description

Over the past half century or so, computer science and mathematical optimization have witnessed the development and maturity of two different paradigms for algorithm design. The first approach, most familiar to computer scientists, is combinatorial in nature. The tools of discrete mathematics are used to understand the structure of the problem, and algorithms effectively exploit this structure to search over a large yet finite set of possible solutions. The second approach, standard in much of the operations research and mathematical optimization communities, primarily employs the tools of continuous mathematics, high dimensional geometry, and convex analysis. Problems are posed as a search over a set of points in high-dimensional Euclidean space, which can can be performed efficiently when the search space and objective function are convex. Whereas many optimization problems are best modeled either as a discrete or convex optimization problem, researchers have increasingly discovered that many problems are best tackled by a combination of combinatorial and continuous techniques. The ability to seemlessly transition between the two views has become an important skill to every researcher working in algorithm design and analysis. This course intends to instill this skill by presenting a unified treatment of both approaches, focusing on algorithm design tasks that employ techniques from both. The intended audience for this course are PhD students, Masters students, and advanced undergraduates interested in research questions in algorithm design, mathematical optimization, or related disciplines.


The main prerequisites for this class are mathematical maturity, a grounding in linear algebra, as well as exposure to algorithm design and analysis at the beginning graduate level (CS570 or 670). Students without such background can seek permission of the instructor.

Requirements and Grading

Homework assignments will count for 75% of the grade. There will be 3-4 assignments, roughly 3 weeks apart each. The homeworks will be proof-based, and are intended to be very challenging. Collaboration and discussion among students is allowed, even encouraged, though students must write up their solutions independently. The remaining 25% of the grade will be allocated to a final project. Students will have to choose a related research topic, read several papers in that area, and write a survey of the area.

Late Homework Policy: Students will be allowed one late homework, at most two days from the due date. No additional late homework will be accepted.


We will refer to two main texts: Convex Optimization by Boyd and Vandenberghe, available free online, and Combinatorial Optimization by Korte and Vygen, available online through USC libraries. Additional references include Combinatorial Optimization by Schrijver, Linear and Nonlinear Programming by Luenberger and Ye, available online through usc libraries, as well as lecture notes from related courses elsewhere. Additionally, we might refer to research papers throughout the course, which will be linked on the course homepage.