BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Peter Zhang (UBC-O hosted) (Carnegie Mellon University) DTSTART:20251118T233000Z DTEND:20251119T003000Z DTSTAMP:20260513T193649Z UID:SFUOR/60 DESCRIPTION:Title: R obust Paths: Geometry and Computation\nby Peter Zhang (UBC-O hosted) ( Carnegie Mellon University) as part of PIMS-CORDS SFU Operations Research Seminar\n\nLecture held in ASB 10908.\n\nAbstract\nApplying robust optimiz ation often requires selecting an appropriate uncertainty set both in shap e and size\, a choice that directly affects the trade-off between average- case and worst-case performances. In practice\, this calibration is usuall y done via trial-and-error: solving the robust optimization problem many t imes with different uncertainty set shapes and sizes\, and examining their performance trade-off. This process is computationally expensive and ad h oc. In this work\, we take a principled approach to study this issue for r obust optimization problems with linear objective functions\, convex feasi ble regions\, and convex uncertainty sets. We introduce and study what we define as the robust path: a set of robust solutions obtained by varying t he uncertainty set's parameters. Our central geometric insight is that a r obust path can be characterized as a Bregman projection of a curve (whose geometry is defined by the uncertainty set) onto the feasible region. This leads to a surprising discovery that the robust path can be approximated via the trajectories of standard optimization algorithms\, such as the pro ximal point method\, of the deterministic counterpart problem. We give a s harp approximation error bound and show it depends on the geometry of the feasible region and the uncertainty set. We also illustrate two special ca ses where the approximation error is zero: the feasible region is polyhedr ally monotone (e.g.\, a simplex feasible region under an ellipsoidal uncer tainty set)\, or the feasible region and the uncertainty set follow a dual relationship. We demonstrate the practical impact of this approach in two settings: portfolio optimization and adversarial deep learning.\n LOCATION:https://researchseminars.org/talk/SFUOR/60/ END:VEVENT END:VCALENDAR