BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hoa Bui (Curtin University) DTSTART:20200708T070000Z DTEND:20200708T080000Z DTSTAMP:20260424T094757Z UID:VAWebinar/4 DESCRIPTION:Title: Zero Duality Gap Conditions via Abstract Convexity\nby Hoa Bui (Curt in University) as part of Variational Analysis and Optimisation Webinar\n\ n\nAbstract\nUsing tools provided by the theory of abstract convexity\, we extend conditions for zero duality gap to the context of nonconvex and no nsmooth optimization. Substituting the classical setting\, an abstract con vex function is the upper envelope of a subset of a family of abstract aff ine functions (being conventional vertical translations of the abstract li near functions). We establish new characterizations of the zero duality ga p under no assumptions on the topology on the space of abstract linear fun ctions. Endowing the latter space with the topology of pointwise convergen ce\, we extend several fundamental facts of the conventional convex analys is. In particular\, we prove that the zero duality gap property can be sta ted in terms of an inclusion involving ε-subdifferentials\, which are sho wn to possess a sum rule. These conditions are new even in conventional co nvex cases. The Banach-Alaoglu-Bourbaki theorem is extended to the space o f abstract linear functions. The latter result extends a fact recently est ablished by Borwein\, Burachik and Yao in the conventional convex case.\n\ nThis talk is based on a joint work with Regina Burachik\, Alex Kruger and David Yost.\n LOCATION:https://researchseminars.org/talk/VAWebinar/4/ END:VEVENT END:VCALENDAR