Convex Analysis and Duality with Applications

Speaker

Prof. Dr. Qiji Jim Zhu (Western Michigan University, USA)

Content

Convex analysis has wide applications in diverse areas. This short lecture series starts with an introduction to the convex analysis and duality. We then explore its applications in optimization, functional analysis, economy and finance. Topics include: separation theorems, linear programming and its duality, linear quadratic optimization problems and Markowitz portfolio theory, utility functions and its applications, the fundamental theorem of asset pricing, as well as coherent risk measures. We will also devote a lecture to mass transport theory and its applications. The material will be structured as eight lectures:

The first three lectures are based on Chapter 4 of J. M. Borwein and Q.J. Zhu, Techniques of Variational Analysis, Springer 2005 and the next 4 lectures are based on P. Carr and Q. J. Zhu, Convex Duality and Financial Mathematics, Springer 2018. The main reference for lecture 8 is C. Villani, Topics in Optimal Transportation, AMS 2003.

Place and time of the lectures

Lectures will take place from 10:30 to 12:00 in Pontdriesch 14-16, Room 008.

Access to the presentation slides

The presentation slides will be uploaded in the RWTHmoodle course room of the Seminar: Convex Analysis and Duality with Applications, to which you will be automatically added when you register for the seminar in RWTHonline. The registration period starts on July 4th and ends on September 30th 2022. Alternatively, you can contact Mr. Kreins (kreins@instmath.rwth-aachen.de), who can either add you manually to the course room or send you the slides by e-mail.

Flyer

We have summarized the most important information about the seminar on a flyer that you can download here.