Robust Semidefinite Programming ∗

In this paper, we consider semidefinite programs where the data is only known to belong to some uncertainty set U . Following recent work by the authors, we develop the notion of robust solution to such problems, which are required to satisfy the (uncertain) constraints whatever the value of the data in U . Even when the decision variable is fixed, checking robust feasibility is in general NP-hard. For a number of uncertainty sets U , we show how to compute robust solutions, based on a sufficient condition for robust feasibility, via SDP. We detail some cases when the sufficient condition is also necessary, such as linear programming or convex quadratic programming with ellipsoidal uncertainty. Finally, we provide examples, taken from interval computations and truss topology design.

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