You’re not where you were, but you’re everywhere we are

It was August 2nd, 2016 at 11:23 pm (European Time) when I received the sad news. I couldn’t believe it and I had read the email twice in the hope that the information was wrong. I couldn’t sleep all night remembering the last time we met with Jon in Cartagena in June 2016 and particularly in all details my last visit to him in Newcastle in February 2015. I will never forget the warm hospitality with which I had been welcomed. I was also thinking about the unfinished paper that we started together with Jon and Lionel entitled: “How elegant modern convex analysis was influenced by Moreau’s seminal work,” which is a tribute to Jean-Jacques Moreau. I was also thinking about Jon’s sense of humor. All those nice jokes we shared together in the car with his wonderful wife Judi during my visit to Newcastle. Every time I told a new joke, Jon started laughing before I finished it. I asked him: “Do you know the joke?” “No, I guessed the punchline,” he answered.

I had known Jon since 1999 during the ceremony of his award “Doctorat Honoris Causa” of the University of Limoges. Thanks to Michel Thera for making Limoges a central meeting place where great mathematicians specialists of Optimization and beyond visited usually. At that time, I was a young associated professor Maitre de Conferences with only two years experience. I was so impressed by Jon’s scientific personality that I couldn’t approach him. But one of the fantastic and exceptional qualities of Jon, are his modesty and his human contact. He made the first step and came to my office asking me which subject I was working on at that moment. My English was not so good, but Jon said: “No problem, continue in French.” Jon knew how to make people comfortable in a conversation.

Another nice moment I remember is during the Second South Pacific Conference on Mathematics in Noumea from August 30 to September 3rd, 2010. I gave a talk about eigenvalue complementarity problems. Just after I finished my talk, Jon came to me and said: “Samir, why don’t you use this equivalence, which transforms your problem to a nonlinear eigenvalue problem, so you can use pseudo-spectral analysis.” I must confess that I did not understand what Jon was trying to say to me and in order to fill the gap, I asked him: “Jon, where can I find a reference for that?” “It’s in my book with Adrian; I will send it to you.” He took his iPad and sent me immediately the entire book in PDF. I took his notes and returned back to my hotel. Since I couldn’t sleep because of the jet lag, I took Jon’s notes and started to understand.

Finally I succeeded to prove the equivalence between the two problems. The originality of this new equivalence, in comparison with the existing literature, is that it is not based on the complementarity approach, i.e. we do not use any NCP-functions. It transforms the eigenvalue complementarity problem to find the eigenvalues of a nonlinear problem. Instead of using fixed-point iteration, as suggested by Jon, I used the semi-smooth Newton method (since I am a big fan of this method). The first numerical simulation with Matlab was successful. The next day I told Jon that his idea was good. He answered me very simply: “Good for you; I’m happy to help.”

I returned to Limoges and I asked my student to compare this method with the most well-known ones in the literature. This method was compared to SNMmin and SNMFB, two algorithms widely discussed in the literature for solving nonlinear complementarity problems. The performance profiles assessment, evaluated on more than 100 benchmark datasets, indicate the efficiency and the robustness of this new method. I did not know what to call this new method, so I sent an email to Jon. Eleven minutes later, I received the following answer: “I would suggest calling it the Lattice Projection Method. JMB in cyberspace.” The paper appeared in Computation Optimization and Applications in 2013 and it was dedicated to Jon for his sixtieth birthday. Jon deserved largely to be a coauthor in this paper but I didn’t dare to ask him. The following quote summarizes Jon’s exceptional scientific qualities: “A great man spreads ideas around him.”

When I was organizing Terryfest 2015 in Limoges, I asked Jon to open the ceremony of this conference dedicated to Terry Rockafellar for his 80th birthday. His speech was absolutely fabulous. You can see the entire video by clicking here.

I am sure that many friends and colleagues who knew Jon, will recognize themselves in this personal testimony. Jon liked collecting quotes and we shared a lot together. He has a blog dedicated to the collection of interesting quotes on science and mathematics. But I want to close this personal testimony with this (slightly modified) quote by Victor Hugo: “Tu n’es plus là où tu étais, mais tu es partout là où nous sommes.” (“You’re not where you were, but you’re everywhere we are.”) [Samir Adly, University of Limoges, France]

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