Robust Optimization is a popular approach to treat uncertainty in optimization problems. Finding a computationally tractable formulation of the robust counterpart of an optimization problem is key in being able to apply this approach. In the first part of the presentation we will give an introduction to Robust Optimization. Although techniques for finding a robust counterpart are available for many types of constraints, no general techniques exist for functions that are convex in the uncertain parameter. Such constraints are, however, common in, e.g., quadratic optimization and geometric programming problems. In the second part of this presentation, we provide a systematic way to construct a safe approximation to the robust counterpart of a nonlinear uncertain inequality that is convex in the uncertain parameters for a polyhedral uncertainty set. We use duality theory as well as adjustable robust optimization techniques to obtain this approximation. We also propose a general purpose method to strengthen the obtained approximation by using nonlinear decision rules for the introduced auxiliary adjustable variables. We show the quality of the approximations by performing several numerical experiments.
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