Seminar in applied mathematics and statistics

SPEAKER: Konstantin Pavlikov (Odense)

TITLE: Tight Formulations for Value-at-Risk Minimization Problems

ABSTRACT: Optimization problems with chance constraints are important both from theoretical and practical standpoints, and generally are hard to solve. Mixed integer problem formulations with big M constants is a standard way to approach such problems, where tightness of such constants is a crucial factor for good performance of a solver. This study focuses on Value-at-Risk minimization, a subclass of chance-constrained optimization problems, and addresses the problem of setting the set of smallest possible big Ms. While finding smallest Ms is computationally intractable, good approximations are possible to obtain within reasonable time. Moreover, we propose a solution methodology that explicitly manages the trade off between computational time spent on finding big Ms and time to solve the original problem. Finally, we discuss possible extensions of this methodology to the more general class of chance-constrained problems.

Tea and chocolate will be served in room 04.4.19 after the seminar.

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Upcoming seminars:

January 11, 15:15: Ryan Tibshirani (Carnegie Mellon)

February 2, 13:15: Axel Munk (Göttingen)

April 6, 13:15: Kayvan Sadeghi (Cambridge)