A Collection of Memorial Messages for the

Anniversary of Professor Alex Rubinov's Passing

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The name of a "Lagrange-type" function is a product of the application of Abstract Convex Analysis to the duality theory of nonconvex/nonlinear programming. Rich theory of the subject can be found in the book "Abstract Convexity and Global Optimization," authored by Alex. Research on Lagrange-type functions and its applications in nonlinear programming is continued by a research group in The Hong Kong Polytechnic University this year. Two papers co-authored with Alex have been published:

--Xiaoqi Yang

SOME MEMORIES DEVOTED TO ALEX

Marco A. L¨®pez, licante University,Alicante (Spain)

I will start by saying that my collaboration in research with Alex and, specially, the friendship that these professional contacts gave rise, is one of the deepest experiences I never had, and one of the reasons that, by itself, convinces me that our job is great, perhaps the best one!

Since long time ago, I was a really impressed by the scientific productivity, and the quality of the numerous papers published by Alex, as well as by the brilliant ideas underlying them, and the many different topics that he approached along the years.

In a wonderful featured talk given by Boris T. Polyak, during the ISMP 2000 in the Georgia Tech (Atlanta), and whose title was ¡°History of Mathematical Programming in the USSR: Analysing the phenomenon¡±, Boris cited a list of outstanding scientists who were the real developers of Mathematical Programming in the former USSR, and Alex was the only one of the list who was still alive!

Aside some previous sporadic personal contacts in different conferences, I invited Alex to deliver a couple of seminars in Alicante & Elche Universities about "Monotonic Analysis¡±. All my colleagues in both universities were delighted with the mathematical beauty of this theory, and we enjoyed the warmness of his personality, as well as the tremendous kindness of his wife Zari. In this occasion Alex suggested to look for some common ground of joint research (min-type functions in monotonic analysis + semi-infinite programming). During my sabbatical year (2003-04), I was expending a couple of months in the Universidad Nacional de Cuyo, in Mendoza (Argentina), and together with Prof. Virginia N. Vera de Serio, we started to work on a draft previously sent (on August 2003) by Alex containing many appealing ideas. In his proverbial modesty, Alex said in his cover message ¡°Please find attached a small draft with some results which can be considered as a base of a joint paper that we discussed in Alicante.  I am waiting for your replies, comments and suggestions. Best regards, Alex.¡±

The ideas given there by Alex were so thoughtful, that we had only to seat down and the results came fluently. We wrote a second draft of about 30 pages, and we sent this material to Alex at the end of October. Alex replied immediately with these words:

¡°I got the files with your very interesting paper and also a message from Marco.  I had a quick look and I like this paper very much. However I could not sign it at this stage since my contribution to the paper is zero. So there are two possibilities: either I should be excluded from the list of the authors or I will add something.  I am not an expert in your field so the latter is not very easy for me. In both cases I will read the paper carefully and give some my comments.¡± Of course, we chose the second possibility, and Alex worked so enthusiastically that in a short time (at the end of 2003) we got a couple of papers [1,2], and what is even more important, we enjoyed very much working with them.

In June 2004, Alex sent to us a new draft as the corner stone of a second project, with some new ideas for further extension of the work previously done, mainly the use of max-type functions.  Virginia and me started to deal with these new ideas and we discussed with Alex our achievements, either by e-mail or personally when I visited Ballarat during ICOTA  (December 9-11, 2004). By the way, ICOTA was a wonderful event, mainly due to the excellent organization and also to the personal attentions devoted by Alex and Zari to all the participants. Finally, we sent to Alex a second version of the draft, with new material, on July 2005. Alex replied a couple of months later and he said: ¡°I am very sorry for the delay with the 'max-type' paper. At last I found time to carefully look at it. I like it very much, however I am still not sure that I can be a co-author, given the exhaustive analysis that has been done by both of you.   Perhaps I can consider the following extensions (if they are of interest)¡­..¡± We were delighted with the fruitful ideas that Alex included in that e-mail, and we decided to work on them. In January 2006 Alex wrote a message in which he informed us about his serious health problems. ¡°Dear Marco and Virginia, Unfortunately I am not well. Some last weeks I had a strong pain on my back ¡­.Finally I got some ideas about a possible extensions of the max-type paper, however I am not sure that I will be able to develop them in the close future. So I suggest that you will publish this paper as it is
without my name. Then, if everything is OK, we will prepare a new paper
on this topic (including perhaps min-type systems as well).¡± Unfortunately, this new paper, planned by Alex, was never written¡­

I would like to conclude just by repeating the words that I addressed to Zari, when Alex passed away ¡°To have met Alex, and to have cooperated in research with him, is the greatest honour and merit in my professional career, and a wonderful lesson about how to behave with the colleagues, the students, etc.¡±  Now I am still more convinced of how much true my statement was.

REFERENCES

1.    M.A. L¨®pez, A. M. Rubinov, and V.N. Vera de Serio,  Stability of semi-infinite inequality systems involving min-type functions, Numerical Functional Analysis and Optimization, Vol. 26(1), pp. 81-112, 2005.

2.    M.A. L¨®pez, A. M. Rubinov, and V.N. Vera de Serio , Stability of the lower level sets of ICAR functions, Numerical Functional Analysis and Optimization, Vol. 26, pp. 113-127, 2005.

On August 26, I made a talk ``Abstract Convexity and Cone-Vexing Abstractions'' at the International Workshop on Idempotent and tropical mathematics in Moscow August 26--30, 2007. Among the listeners were Professor Zinger and Professor Tikhomirov
whom you surely know. I dedicated this talk to memory of my late friend and coauthor and said a few word about his contributions to the field.
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--Semen Kutateladze, Sobolev Institute of Mathematics, Novosibirsk State University
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It is difficult to believe that it has been a year since Alex passed away. It seems that he is still with us: his papers are published, his talks are presented by his collaborators, his work is in progress. While doing mathematics, I often say automatically to myself ¡°I should share this with Alex, I should discuss this with Alex.¡± But we cannot do it anymore¡­

Besides his tremendous mathematical legacy and his strong mathematical school, Alex Rubinov left to us certain issues that cannot be counted by a number of brilliant results and successful students: his decency, his dignity, his courage, his kindness, his understanding and compassion and much, much more. He got terminally sick at the pick of his life, full of strength and ideas, probably at one of his happiest periods. And we will always remember him at this pick.

--Boris Mordukhovich

Dear Zari, (About Alex Rubinov PhD Scholarship), this is wonderful news.  It's a very fitting tribute to Alex. Just now I'm in Alicante, Spain, at a meeting with Juan-Enrique and others.  He and I have thought about this anniversary of Alex's passing
and how much has been lost, and how difficult it still is for you, of course.  As you know, I wrote, with some input from Juan-Enrique, the preface to the volume of papers dedicated to Alex which will be published soon. 

With warmest regards,

-Terry

Dear Zari, It is wonderful that you and the friends are memorizing Alex so faithfully and, by this, preserve and use his precious heritage to the best of all of us, of the next generation!

In these days, we work for EURO XXIII 2009 in Bonn already. As I discussed with the POP leaders, I am trying to keep POP
as close as possible to the name of our EURO Working Group EUROPT, whenever our streams are listed. I wish that this will
be done on the conference homepage also. Then a similar situation as in Iceland 2006 would be given - there we had a
great common success, mainly based on the fruitful collaboration with Alex. In this tradition - the one of Alex - we will proceed.

In addition, since we both and other friends met and exchanged in Prague, I am going on with reminding and hopefully preparing that our next great EURO conference should have a very nice, personal and hospitable character for, if possible, everyone going to come.

with my warmest regards

Willi

I met Alex in 2004 in Rhodes at the EUROPT meeting. Since then we have started very quickly research collaboration with him and with Adil. Non-smooth optimization was a new reserach field for our  Institute of Applied Mathematics at the Middle East Technical University, Ankara. Our collaboration  with Adil Bagirov, Yalcin Kaya and Regina Burachick now continues in form of mutual visits, conference attendances etc. All these were not possible without the great personality of Alex. I
remember also very well the warm hospitality of Zari 1993 when we as a group of Turkish mathematicians visit Baku.

Bulent Karasozen
Department of Mathematics & Institute of Applied Mathematics
Middle East Technical University
Ankara-Turkey

Dear Zari, I am really not good at public speeches, nor writings. But please do not have the impression that this sad anniversary passes away without a small piece of thinking about Alex.

You know how much I loved him and what a strong impact his personality and his research had and still have on my personal and professional life.

I will always do whatever is in my possibility to carry on his human and scientific teachings.

yours

Alberto

Dear Zari, As you know, Yalcin and I are working (and living) in METU until mid October. We walk to the Applied Mathematics Institute every day, crossing a very nice forest in the Campus. Yalcin and met Alex in this
same forest in METU in 2004, so walking here is yet another way of remembering him, and keep his company close to us.
 
Alex taught me that mathematics can be much more than just a list of technical facts. He showed us how mathematics can be understood also as a wonderful network of people, countries and ideas, and that each theorem and each definition is intrinsically connected with the people and the circumstances that generated them. He gave me a Polaroid photo
(taken in the seventies) of Bregman and himself in Novosibirsk the day I gave a talk using Bregman distances in SAMOS in 2000. That day was the first time I met Alex, and he stayed as sweet as that time on every occasion since then.
 
I want you to know that all my thoughts are all the time with you, Elder and Mika, I am sending you all my love.

--Regina.

Dear Zari, One year passed since Alex departed, which I still remember very sadly.  METU was one of the many places Regina and I met him - it was a very hot day in July 2004 when we joined him at a Summer workshop at METU and then went to a roof-top restaurant at the campus to have lunch together.  I am attaching two photos showing us together in the restaurant.  I am writing this short letter to you from METU, where Regina and I are doing research until the middle of October.  At the moment we are staying near the Guesthouse where Alex also stayed in July 2004.
 
It was always pleasant to have a conversation with Alex, and it wasn't restricted to just mathematical or academic issues.  I remember talking with him in that roof-top restaurant about the political system in the Soviet Union as he witnessed it himself during the time he lived in the USSR.  He was telling us that the communist system might be a nice utopia but it is impossible to achieve it because of the nature humans have.  He held the view that in their efforts for achieving their
utopias, humans are constrained with their personal ambitions, such as their aspiration to move to the top, to rule others, etc.  Alex was one of the humblest people I have ever seen, so what he commented on about the human nature made me think that maybe he was seeing the human pretention of being "more important than others" as an obstacle for the well-being of everyone.
 
Waking up this morning, on the first anniversary of Alex's leaving, in METU where Alex spent time on several occasions, we felt more intensely of a beautiful human being who still has a comforting influence on us.
 
Dear Zari, our thoughts are always with you.  Please give our warm regards to Eldar and Michael.
 
--Hoscakal, Yalcin
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