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Distributionally Robust Optimization with SOS Polynomial Density Functions and Moment Conditions

Banff International Research Station for Mathematical Innovation and Discovery

Numerous decision problems are solved using the tools of distributionally robust optimization. In this framework, the distribution of the problem's random parameter is assumed to be known only partially in the form of, for example, the values of its first moments. The aim is to minimize the expected value of a function of the decision variables, assuming the worst-possible realization of the unknown probability measure. In the general moment problem approach, the worst-case distributions are atomic. We propose to model smooth uncertain density functions using sum-of-squares polynomials with known moments over a given domain. We show that in this setup, one can evaluate the worst-case expected values of the functions of the decision variables in a computationally tractable way. Joint work with Etienne de Klerk and Daniel Kuhn.

Mathematics; Operations research, mathematical programming; Probability theory and stochastic processes; Operation research

video/mp4

Author affiliation: Erasmus University Rotterdam

2018-09-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67063

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/