BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Ulbrich (Technical University of Munich) DTSTART:20210412T133000Z DTEND:20210412T143000Z DTSTAMP:20260423T021012Z UID:OWOS/43 DESCRIPTION:Title: An Approximation Scheme for Distributionally Robust Nonlinear Optimization w ith Applications to PDE-Constrained Problems under Uncertainty\nby Mic hael Ulbrich (Technical University of Munich) as part of One World Optimiz ation seminar\n\n\nAbstract\nWe present a sampling-free approximation sche me for distributionally robust nonlinear optimization (DRO). The DRO probl em can be written in a bilevel form that involves maximal (i.e.\, worst ca se) value functions of expectation of nonlinear functions that depend on t he optimization variables and random parameters. The maximum values are ta ken over an ambiguity set of probability measures which is defined by mome nt constraints. To achieve a good compromise between tractability and accu racy we approximate nonlinear dependencies of the\ncost / constraint funct ions on the random parameters by quadratic Taylor expansions. This results in an approximate DRO problem which on the lower level then involves valu e functions of parametric trust-region problems and of parametric semidefi nite programs. Using trust-region duality\, a barrier approach\, and other techniques we construct gradient consistent smoothing functions for these value functions and show global convergence of a corresponding homotopy m ethod. We discuss the application of our approach to PDE constrained optim ization under uncertainty and present numerical results.\n\nThe address an d password of the zoom room of the seminar are sent by e-mail on the maili nglist of the seminar one day before each talk\n LOCATION:https://researchseminars.org/talk/OWOS/43/ END:VEVENT END:VCALENDAR