BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:R. Tyrrell Rockafellar (University of Washington) DTSTART:20201012T133000Z DTEND:20201012T143000Z DTSTAMP:20260423T035027Z UID:OWOS/21 DESCRIPTION:Title: Au gmented Lagrangians and Hidden Convexity in Sufficient Conditions for Loca l Optimality\nby R. Tyrrell Rockafellar (University of Washington) as part of One World Optimization seminar\n\n\nAbstract\nSecond-order suffici ent conditions for local optimality have long been central to designing so lution algorithms and justifying claims about their convergence. In this talk a far-reaching extension of such conditions\, called variational suff iciency\, will be explained in territory beyond just nonlinear programming . Variational sufficiency is already known to support multiplier methods that are able\, even without convexity\, to achieve problem decomposition\ , but further insight has been needed to see how it coordinates with other sufficient conditions. In fact it characterizes local optimality in term s of having a convex-concave-type local saddle point of an augmented Lagra ngian function. \n\nA stronger version of variational sufficiency corresp onds in turn to local strong convexity in the primal argument of that func tion and a property of augmented tilt stability which offers crucial aid t o Lagrange multiplier methods at a fundamental level of analysis. Moreove r\, that strong version can be translated through second-order variational analysis into statements which may readily be compared to existing suffic ient conditions in nonlinear programming\, second-order cone programming\, and other problem formulations that are able to incorporate nonsmooth obj ectives and regularization terms.\n\nthe address and password of the zoom room of the seminar are sent by e-mail on the mailinglist of the seminar o ne day before each talk\n LOCATION:https://researchseminars.org/talk/OWOS/21/ END:VEVENT END:VCALENDAR