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Is DRO the Only Approach for Optimization Problems with Convex Uncertainty?

Banff International Research Station for Mathematical Innovation and Discovery

Uncertain constraints with convex uncertainty are in general difficult to tackle for "normal" RO. However, several DRO approaches are well suited for such cases. In this talk we first discuss two of such DRO approaches. Then, as a non-DRO alternative, we propose an RO method to obtain approximate solutions for some problems with convex uncertainty and polyhedral uncertainty region. For example, an uncertain SOC constraint with polyhedral uncertainty is reformulated as an adjustable robust linear optimization problem with ellipsoidal uncertainty region, for which linear and non-linear decision rules can be used to obtain approximate solutions. For two numerical examples it appeared that linear decision rules already lead to (near) optimal solutions.

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

video/mp4

Author affiliation: Tilburg University

2018-09-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67096

Unreviewed

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