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Tuesday, 22 April 2014

Guest speaker: 

Generalized Gauss Inequalities via Semidefinite Programming

Speaker:  Bart Van Parys
Biografie :
"Bart Van Parys received the B.A. degree in electrical engineering and the M.A. degree in applied mathematics, both from the University of Leuven, Belgium. He is currently pursuing the Ph.D. degree at the Swiss Federal Institute of Technology (ETH Zürich), Zürich, Switzerland, under the supervision of Prof. Morari."
Location:  Room C
Time:  10:45 until 12:45
Abstract:  A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. These bounds are widely used across many different application domains, ranging from distributionally robust optimization to chance-constrained programming, stochastic control, machine learning, signal processing, option pricing, portfolio selection and hedging. However, these Chebyshev-type bounds tend to be overly conservative since they are determined by a discrete worst-case distribution. In this talk we present a less pessimistic Gauss-type bound by imposing the additional requirement that the random vector’s distribution must be unimodal. We show that this generalized Gauss bound still admits an exact and tractable semidefinite representation. Moreover, we demonstrate that both the Chebyshev and Gauss bounds can be obtained within a unified framework using a generalized notion of unimodality. We also offer new perspectives on the computational solution of generalized moment problems, since we used concepts from Choquet theory instead of traditional duality arguments to derive semidefinite representations for worst-case probability bounds."

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Last modified: 21 March 2014, 15:20 UTC
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