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DTSTART;TZID=Europe/Berlin:20221128T160000
DTEND;TZID=Europe/Berlin:20221128T170000
DTSTAMP:20221216T110700Z
CREATED:20221025T102708Z
LAST-MODIFIED:20221216T110700Z
UID:6801-1669651200-1669654800@alop.uni-trier.de
SUMMARY:ALOP Colloquium with Martina Cerulli
DESCRIPTION:On Monday\, November 28 2022 at 16:00 c.t. Martina Cerulli\, ESSEC Business School of Paris\, will speak at the ALOP Colloquium about her recent work: \n  \nOn the dualization of the inner problems of Semi-Infinite programs \nAbstract: \nIn this talk\, we will discuss a solution approach for Semi-Infinite programs (SIPs) based on the dualization of the inner problem\, i.e.\, the problem of finding the constraint that is the most violated by a given point. After a brief introduction to SIPs and the classical solution techniques for these optimization programs\, we will consider two practical problems that can be modeled as SIPs: the aircraft conflict resolution and the collapsed k-core problem. Then\, we will present the results of the paper “Convergent algorithms for a class of convex semi-infinite programs” by M. Cerulli\, A. Oustry\, C. D’Ambrosio\, L. Liberti\, accepted for publication on SIAM Journal on Optimization. In this paper\, we focus on convex SIPs with an infinite number of quadratically parametrized constraints\, not necessarily convex w.r.t. the parameter. A new convergent approach to solve these SIPs is proposed\, leveraging the dualization technique. Based on the Lagrangian dual of the inner problem\, a convex and tractable restriction of the considered SIP is derived. We state sufficient conditions for the optimality of this restriction. If these conditions are not met\, the restriction is enlarged through an Inner-Outer Approximation Algorithm\, and its value converges to the value of the original semi-infinite problem. This new algorithmic approach is compared with the classical Cutting Plane algorithm. We propose a new rate of convergence of the Cutting Plane algorithm\, directly related to the iteration index\, derived when the objective function is strongly convex\, and under a strict feasibility assumption. We successfully test the two methods on two applications: the constrained quadratic regression and a zero-sum game with cubic payoff.  \nPlease join us at 16:00 c.t. in HS 9.
URL:https://alop.uni-trier.de/event/alop-colloquium-with-martina-cerulli/
LOCATION:Trier University E Building\, Universitätsring 15\, Trier\, 54296\, Germany
CATEGORIES:Colloquium
ORGANIZER;CN="RTG ALOP at Trier University":MAILTO:ALOP@uni-trier.de
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