ALEX M. RUBINOV

Rubinov was born on March 28, 1940 in St. Petersburg. His father was a college teacher and his mother worked in a court of justice. Rubinov graduated from high school in 1957 and was admitted to the Physics and Mathematics Department of the Leningrad State Pedagogical Institute. In 1958 he arranged his transfer to Leningrad State University. He graduated from the Department of Mechanics and Mathematics in 1962 and entered into his post graduate study in functional analysis. His supervisor was Gleb Akilov, a student and coauthor of Leonid Kantorovich. In these years Rubinov started his lifelong collaboration with Vladimir Demyanov. They were involved then in application of functional analysis to optimization and numerical methods.

Kantorovich joined the Siberian Division of the Academy of Sciences which was organized in 1957 and moved to Novosibirsk. Akilov followed his tutor and so did Rubinov. From June of 1964 he was on the staff of the Mathematical–Economic Department headed by Kantorovich, continuing his postgraduate study distantly in Leningrad State University. In May of 1965 he maintained his thesis “Minimization of Convex Functionals on Some Classes of Convex Sets in Banach Spaces” and received the Kandidat Degree.

The “Siberian period” formed the main areas of Rubinov's research. He narrated this in one of his last interviews as follows:

- My first book: “Approximate Methods in Optimization Problems” (with V.F. Demyanov) was written in 1966–1967 and published in 1968.
- My second book “Mathematical Theory of Economic Dynamics and Equilibria” (with V.L. Makarov) was written in 1968–1970 and published in 1973.
- My third book “Minkowski Duality and Its Applications” (with S.S. Kutateladze) was written in 1970–1972 and published in 1976.
*My research interests are mainly concentrated around indicated fields: Optimization, Mathematical economics, Abstract convexity. (It seems that “Minkowski Duality” was the first book in the world dedicated to abstract convexity.) I also work in related topics. I tried to contribute to economics (one of my text books is called “Elements of Economic Theory (a textbook for students of mathematical departments)” (with A. Nagiev), I had some papers and books in nonsmooth analysis (quasidifferential calculus, jointly with V.F. Demyanov), some papers in dynamical system theory etc. Last years I am involved in application of optimization to data analysis and telecommunication.*

Rubinov chose his scientific itinerary in his green years and travelled along the route up to his terminal day.

In 1970 Rubinov was on his rapid creative uprise—he submitted and maintained the doctorate thesis “Point-to-Set Mappings Defined on Cones.”

The defence took place in Novosibirsk and was quite a success. So the chances were very high that the degree would be awarded by the Higher Attestation Committee in Moscow. The Committee sent Rubinov's thesis to Nikita Moiseev for giving an official “blind” review, which was a standard procedure. Moiseev rang to Rubinov, which was in violation of the procedure, and told Rubinov that he would give a favorable review. Moiseev was a corresponding member of the Academy of Sciences of the USSR and was interested in good relations with Kantorovich who was an influential full member. After the call Rubinovs decided to move from Novosibirsk back to European Russia right away, not awaiting the Moscow decision on the new degree which would open many favorable positions for Rubinov. This was hasty but it was not Rubinov's own choice. He was under the pressure of his family. But the plans to return to the Northern capital of Russia failed, and Rubinovs moved to Tver (then Kalinin) which is between Moscow and St. Petersburg. Rubinov found a position in Kalinin State University which was then an asylum for the capable mathematicians mostly of Jewish origin who could not find positions in Moscow and Leningrad. When Moiseev became aware of the departure of Rubinov from Novosibirsk, which was groundlessly interpreted as the end of Kantorovich's interest in Rubinov's fate, Moiseev lost his compassion to Rubinov and abstained from giving any review.

These years in the academic life of the USSR were poisoned with careerism whose most disgusting manifestation was Anti-Semitism. Quite a few “successful” figures of the epoch were so unscrupulous that traded over xenophobia and other similar techniques of emptying the career lane. Rubinov suffered from these deceases of the Soviet life for many years. The pressure on him was aggravated by this refusal of Moiseev. In result, Rubinov decided to vacate his thesis formally to ensure his family from loosing everything had he continued asking for the doctorate. Of course, Rubinov's cautious surrender was a relief to his academic adversaries and native Anti-Semites.

A few years later Rubinov found a modest position in Leningrad. He was supported by his friends and began to work at the Institute for Social-Economic Problems in the laboratory headed by Nikolai Vorob'ëv. Rubinov wrote a new thesis for his doctorate in demography but it turned out impossible to arrange the official defence in the rotten atmosphere of the academic life of the USSR.

Rubinov received his Doctor degree only in 1986 after maintaining his thesis in the Computer Center of the Academy of Sciences of the USSR. Moiseev had become a full member of the Academy in 1984, his career was crowned, and he supported Rubinov this time.

In 1988 Rubinov moved to Azerbaijan where he worked successfully in the Institute of Mathematics and Baku State University. After disintegration of the USSR Rubinov emigrated to Israel where he spent a few years in the Ben-Gurion University of the Negev. In 1996 Rubinov moved to Australia and took a position in Ballarat University where he worked up to his untimely death from cancer on September 9, 2006.

The creative talent of Rubinov had blossomed in his “Australian period.” His efforts made Ballarat a noticable world center of global optimization and nonsmooth analysis. In 2006 the European Working Group on Continuous Optimization chose Rubinov as a EUROPT Fellow 2006.

Rubinov was an outstanding example of the working mathematician.
He contributed to the theory and numerical methods of optimization.
He developed the technique of studying the sublinear functionals that are
defined and monotone on a cone. He elaborated the duality technique for them
which belongs to subdifferential calculus.
Rubinov paid much attention to abstract local convex analysis to quasi-differentiable functions
whose derivatives can be represented as differences of sublinear functionals.
Rubinov was one of the leading figures in abstract convexity—he extended duality
to the upper envelopes of the subsets of some given family *H* of simple functions.
The conception of *H*-convexity happened to be tied with the deep
problems of Choquet theory and approximation by positive operators through the
new concept of supremal generator.
Rubinov invented monotonic analysis. He gave the nicest form for the
theorem of characteristics of optimal trajectories of models of economic dynamics and
other discrete dynamic problems. His research enriched the important
section of mathematical economics whose progress was connected with
the theory of convex processes by
John von Neumann,
David Gale, and
Terry Rockafellar.
Rubinov published about twenty books and more than 150 papers.
But what stands above all Rubinov's scientific contributions
is his path of academic service impeccable despite all obstacles
and pits of his rough worldline.

Rubinov remains in the memory of those who knew and understood him not only a prominent scholar but also a brilliant, loving, faithful, and charming personality.

June 21, 2012

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© Кутателадзе С. С. 2012