Abstract
Adjustable Robust Optimization (ARO) yields, in general, better worstcase solutions than static Robust Optimization (RO). However, ARO is computationally more difficult than RO. In this talk, we derive conditions under which the worstcase objective values of ARO and RO problems are equal. We prove that if the uncertainty is constraintwise and the adjustable variables lie in a compact set, then under one of the following sets of conditions robust solutions are optimal for the corresponding (ARO) problem:
(i) the problem is fixed recourse and the uncertainty set is compact,
(ii) the problem is convex with respect to the adjustable variables and concave with respect to the parameters defining constraintwise uncertainty.
Furthermore, if we have both constraintwise and nonconstraintwise uncertainty, under similar sets of assumptions we prove that there is an optimal decision rule for the Adjustable Robust Optimization problem that does not depend on the parameters defining constraintwise uncertainty. Also, we show that for a class of problems, using affine decision rules that depend on both types of uncertain parameters yields the same optimal value as ones depending solely on the nonconstraintwise uncertain parameter. Additionally, we provide several examples not only to illustrate our results, but also to show that the assumptions are crucial and omitting one of them can make the optimal worstcase objective values different.
.
Information:
Date and Time:  Tuesday, January 12, 2016, 14:0017:00
 Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
