**Tuesday, 15:45 - 16:10 h, Room: MA 042**

**Bram Gorissen**

Tractable robust counterparts of linear conic optimization problems via their duals

**Coauthors: Aharon Ben Tal, Hans Blanc, Dick Den Hertog**

**Abstract:**

We propose a new way to derive the tractable robust counterpart of a linear conic optimization problem.

For the dual of a robust optimization problem, it is known that the uncertain parameters of the primal problem become optimization variables in the dual problem ("primal worst is dual best''). We give a convex reformulation of the dual problem of a robust linear conic program. When this problem is bounded and satisfies the Slater condition, strong duality holds. We show how to construct the primal optimal solution from the dual optimal solution. Our result allows many new uncertainty regions to be considered that were previously intractable, e.g., the set of steady state probability vectors of a Markov chain with uncertain transition probabilities, or the set of vectors whose Bregman or phi-divergence distance to a given vector is restricted. Our result also makes it easy to construct the robust counterpart for intersections of uncertainty regions. The description of the uncertainty region is in the constraints of the dual optimization problem, so using intersections of uncertainty regions is as simple as adding constraints for all uncertainty regions involved.

Talk 2 of the invited session Tue.3.MA 042

**"Theory of robust optimization"** [...]

Cluster 20

**"Robust optimization"** [...]