The study of convex optimization and convex analysis in general dates back to antiquity. However, a systematic study began in the early 20th century. The development of the subject accelerated significantly in the last half century, and there has been an explosion of new develpments and applications within the last 25 years. This rapid growth continues today with no end in sight. Just within the past 10 years at least 20 news texts have been written on the topic, all making different contributions and providing different perspectives on the topic.

Many factors have contributed to the enormous growth of this topic. The most important of these are (1) the mathmatical foundations of the subject are now well developed, (2) new numerical methods exist for the accurate and rapid solution of a wide range of convex optimization problems, and (3) new modeling paradigms have been developed permitting the modeling or approximation of an enourmous range of applied problems in engineering, finance, computational geometry, and management science.

In this course, we develop some of the foundations of the subject, mostly from the analytic, as opposed to the geometric/algebraic, perspective. Our first goal is the development of convex duality from various perspectives. With this foundation, we then study a range of questions, models, and problems from the last 20 years or so. Much this mathematics finds its basis in applications in engineering, finance, and statistics.

Course Notes

LP Notes

Home Work

Mathematics Department

University of Washington