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Advanced Optimization Laboratory Title : Bi-Parametric Convex Quadratic Optimization

In this paper we consider the Convex Quadratic Optimization problem with simultaneous perturbation in the right-hand-side of the constraints and the linear term of the objective function with different parameters. The regions with invariant optimal partitions are investigated as well as the behavior of the optimal value function on the regions. We show that identifying these regions can be done in polynomial time in the output size. An algorithm for identifying all invariancy regions is presented. Some implementation details, as well as a numerical example are discussed.