Tuesday, 15:15 - 15:40 h, Room: MA 042

 

Dick Den Hertog
Deriving robust counterparts of nonlinear uncertain inequalities

Coauthors: Aharon Ben-Tal, Jean-Philippe Vial

 

Abstract:
We provide a structured way to construct the robust counterpart for a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function. Surprisingly, these two computations are completely independent. This approach has several advantages. First, it provides an easy, structured, way to construct the robust counterpart both for linear and nonlinear inequalities. Second, it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived. Third, it paves the way to a new, more flexible, Globalized Robust Counterpart approach.

 

Talk 1 of the invited session Tue.3.MA 042
"Theory of robust optimization" [...]
Cluster 20
"Robust optimization" [...]

 

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