My memories of Jon Borwein

I first met Jon Borwein at an Optimization Day workshop at Ballarat University, Australia, in 1999. I was immediately impressed by the power and clarity of Jon’s expertise in convex analysis and optimization. His presentations were always entertaining and insightful. His books are little treasures. The breadth of his knowledge was enormous—not only in relation to the subject matter itself but also to the history and wider relevance of the topic. Jon’s sense of humour was acute. I’m not sure which talk it was—possibly an invited lecture at the annual conference of the Australian Mathematical Society (Aust MS)—but I remember vividly his slide depicting The Institute of Solid Geometry, an imposing conventional building next door to a large billboard labelled The Institute of Plane Geometry. One always wondered if there was something profound in these humorous observations.

Jon was a good man. When I approached him in 1999 about a visit to the Centre for Industrial and Applied Mathematics (CIAM) at the University of South Australia he didn’t hesitate to accept—although at that stage he barely knew me. The visit was a big deal for us but for Jon it was surely an act of professional support for a new University and a fledgling organisation. Of course Jon knew that mutual support was ultimately a good thing for the whole mathematics community and so it was a tribute to his good sense as well as his good nature. Although this first visit did not lead directly to any joint research it certainly laid the foundations for future collaborations. In the first instance Jon agreed to act as a referee for an application to the Australian Research Council to fund an Australian network for Industrial and Applied Mathematics. Although Jon and the other referees gave our application very strong support we were not successful. Nevertheless I see this in retrospect as a small setback in a continuing successful development of applied mathematics in Australia. Later, when Jon moved to the University of Newcastle in New South Wales to set up his beloved Centre for Computer-Assisted Research Mathematics and its Applications (CARMA)—and during my time as Chairman of the Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) group—I was able to support his application to form a Special Interest Group, SigmaOpt within ANZIAM. SigmaOpt is now an active national group that runs regular Australia wide seminars and organises major optimization conferences. In many ways it has become the backbone of the optimization community in Australasia. Jon’s leadership of both CARMA and SigmaOpt will be sadly missed.

My research collaboration with Jon was relatively minor on the grand scale of all things optimal. My colleague, Julia Piantadosi and I had introduced the idea of a checkerboard copula of maximum entropy to model joint rainfall distributions in such a way that the marginal distributions could be modelled by gamma distributions—the preferred model for such distributions—and so that the observed correlations between the marginal distributions could also be matched. We had formulated the problem as a maximization of entropy subject to a collection of linear constraints. After a presentation of this work at Aust MS Jon pointed out to us that such problems could be very neatly solved as unconstrained problems using the theory of Fenchel duality. We subsequently published several joint papers with Jon on this topic—most notably in Optimization Letters, in Numerical Algebra, Control, and Optimization (NACO) and in Entropy. Indeed at the time of Jon’s death we had just initiated plans to follow up on another related suggestion that Jon had made about maximum entropy copulas with matching higher order moments. Time will tell if we can now complete this work in his memory.

I could probably go on—but I’m not sure what that would achieve. I remember fondly good times that my wife Lori and I had with Judy and John when they visited us in Adelaide circa 2001 and again a few years later when we caught up with them in Sydney. They were a real team. On a professional level Jon certainly made his mark on mathematics worldwide. We can say with complete conviction that he was and therefore he is. Jon was my friend and to my mind he is out there somewhere in another dimension. In his own words, “JMB in cyberspace.” [Phil Howlett, Emeritus Professor, Industrial and Applied Mathematics, University of South Australia]

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