**SIGMAOPT SEMINAR/OCANA SEMINAR****Location:**Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle**Dates:**9:30 am, Tue, 28^{th}Jul 2015 - 11:00 am, Tue, 28^{th}Jul 2015
**Jon's talk will be 60 minutes, followed by 30 minutes for Yves.****Speaker:**Laureate Prof Jon Borwein, CARMA, The University of Newcastle**Title:***Monotone inclusions and Fitzpatrick functions*- We also study the special cases of a variational inequality and of a generalised variational inequality problem.
- The associated notion of a scalar gap is also considered.
- Corresponding local and global error bounds are developed for the maximal monotone inclusion.
**Speaker:**Yves Lucet, University of British Colombia**Title:***On the convexity of piecewise-defined functions***[Permanent link]**
We study maximal monotone inclusions from the perspective of (convex) gap functions. We propose a very natural gap function and will demonstrate how this function arises from the Fitzpatrick function — a convex function used effectively to represent maximal monotone operators. This approach allows us to use the powerful strong Fitzpatrick inequality to analyse solutions of the inclusion. This is joint work with Joydeep Dutta. Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components – when can we conclude that the entire function is convex? Our main result provides sufficient conditions for a piecewise-defined function f to be convex. We also provide a sufficient condition for checking the convexity of a piecewise linear-quadratic function, which play an important role in computer-aided convex analysis. Based on joint work with Heinz H. Bauschke (Mathematics, UBC Okanagan) and Hung M. Phan (Mathematics, University of Massachusetts Lowell). |