1.    Your full name, address and e-mail address:

      Rubinov Alexander   (in Russian: Rubinov Alexandr Moiseevich)

2.  Your highest degree, awarding institution and year:

     Doctor of Science, Computer Centre USSR Academy of Science, Moscow, granted  by  USSR High Attestation Board, 1985.       

3.  How many books and research papers have you published (including papers accepted for publication).  How many of them in the field of optimization?

4.  Your research interests:   

   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.

  From 1975 till 1994 I was mainly engaged in Mathematical Economics. (Of course I was involved also in some different topics, for example quasidifferential calculus was invented by V.F. Demyanov and myself in 1979. )    I was one of the leading experts in the field of mathematical economics in former Soviet Union. When I immigrated from former SU in 1993, I tried to continue my research in this area, however   mathematical economic community on the West did not want not accept me.  I had some interesting ideas, and it is a pity that I could not realize them.  On the other hand I feel that some modern approaches to mathematical theory of economical dynamics are not very good from the economical point of view, moreover some generally accepted notions in modern mathematical economics deserve criticism.  

  In contrast with mathematical economics, members of optimization community were very friendly and helped me a lot.  I am very thankful to them.  So I turned to optimization and its applications and to abstract convexity and I have mainly working in these areas from 1994.

 5. Some of your most representative papers or books:

 I give the list of my monographs (Books 1- 6 and 8-10 were written in Russian and books  7 and 11-14 were written in English):

[1]  V. F. Demyanov and A.M. Rubinov, Approximate Methods in Optimization Problems,  Leningrad University Press, 1968, 180pp. ( There is an English translation: Modern Analysis and Computational Methods in Science and Mathematics, No 32, America Elsevier Publ.Comp., New York, 1970, ix + 256pp.)

[2]  V. L. Makarov and A.M.Rubinov, Mathematical Theory of Economic Dynamics and  Equilibria, Nauka, Moskow, 1973, 335pp. ( There is an English translation: Springer-Verlag, 1977, xv + 252pp.) 

[3]  S. S. Kutateladze and  A. M. Rubinov,  Minkowski Duality and its Applications, Nauka, Novosibirsk, 1976, 254pp.

[4]  A. Ya. Kiruta, A. M. Rubinov and E. B. Yanovskaya, Optimal Choice of Distributions in Complex Social-Economic Problems, Nauka, Leningrad, 1980, 166pp.

[5]  A. M. Rubinov,  Superlinear Multivalued Mappings and Their Applications to Problems of Mathematical Economics, Nauka, Leningrad, 1980, 165pp.

[6]   A. M. Rubinov, Mathematical Models of Expanded Reproduction, Nauka, Leningrad, 1983, 187pp.

[7 ]  V. F. Demyanov, A. M.Rubinov, Quasidifferential Calculus, Optimization Software, Inc. Publications  Division, New-York, 1986, 288pp.

[8]   V. F. Demyanov and A. M. Rubinov, Foundations of Nonsmooth  Analysis, and  Quasidifferential Calculus, Optimization and Operation Research, v. 23, Nauka, Moscow, 1990, 431pp.

[9]  A. M. Rubinov, K. Yu. Borisov, V. N. Desnitskaya and V. D. Matveenko, Optimal Control in Aggregated Models of Economics,  Nauka,  Leningrad,  1991, 269pp.

[10]  M.J.Levin, V.L. Makarov and A. M. Rubinov, Mathematical Models of Economic Interaction, Theory and Methods of Systems Analysis, v.29,  Nauka, Moscow, 1993, 374pp.

[11]  V.F. Demyanov and A.M. Rubinov, Constructive Nonsmooth Analysis, Approximation and Optimization, No 7,  Peter Lang, Frankfurt am Main, 1995, iv + 416pp. (this is an extended and modified version of a part of the book 8.)

[12]  V.L. Makarov, A.M. Rubinov and  M. J. Levin , Mathematical Economic Theory: Pure and Mixed Types of Economic Mechanisms, Advanced Textbook in Economics, v.33, North-Holland Publishing Co., Amsterdam - New York, 1995, xx +610 pp (this is an extended and modified version of  the book 10). 

[13]  A. M Rubinov, Abstract Convexity and Global Optimization, Kluwer Academic Publishers, 2000, vii + 490 pp.

[14]  A.M. Rubinov  and X.Q. Yang, Lagrange-type functions in constrained non-convex  optimization, Kluwer Academic Publishers, 2003., xi + 286 pp.

 I also include two survey papers:

[15] A. M. Rubinov,  Sublinear Operators and their Applications, Uspehi Mat. Nauk, (Russian  Math. Surv.), vol. 32 , 113-174, 1977.

[16] A.M. Bagirov,  A. M. Rubinov, N.V. Soukhoroukova and J. Yearwood,  Unsupervised and supervised data classification via nonsmooth and global optimization, TOP (Journal of Spanish Operations Research Society),  vol. 11, pp. 1-75, 2003

 6. Please describe your major contributions in optimization:

 Terry Rockafellar said in one of his interviews that there are two types of mathematicians: problem-solvers and theory-builders.   I am a theory-builder, so my major contributions consist of some theories in optimization and related topics.  I mention the following (in the chronological order):

 Quasidifferential calculus (with  V. F.  Demyanov).  There is a lot of misunderstanding here. Quasidiferential calculus does not provide a special kind of approximation of a nonsmooth function.  This is exactly calculus which allows one to calculate an exact linearization of approximation for many functions. From a certain point of view this is not important, so many experts who are not engaged in nonsmooth and nonconvex numerical optimization, do not consider it as a serious achievement. However, many of those, who are engaged, do consider.  It was shown by Adil Bagirov, that  combinations of  quasidifferentiability and semismothness give good numerical methods for solving some complicated problems.      

 Cutting angle method (with M. Andramonov, B. Glover , A. Bagirov).  This a version of the cutting plane method that can be used for global optimization of a Lipschitz function over a simplex.  This is a real application of abstract convexity (through monotonic analysis) to global optimization.      A combination of the cutting angle method with some local methods (DG + CAM)  developed by Adil Bagirov and myself  is a very efficient heuristics for solving  nonsmooth problems of global optimization in high dimensions.

 Non-linear Lagrange-type functions (with X.Q. Yang and R. Gasimov).    Non-linear Lagrange functions are an efficient tool for solving constrained non-convex optimization problems.    Such main notion of this theory as the zero duality gap and exact multipliers (penalty parameters) can be examined by means of abstract convexity which gives a simple and transparent explanation of many results related to these notions.   Monotonic analysis can be used in the study of special penalty- type functions.

 Currently I am engaged in monotonic analysis. I am working in this area with some of my friends (J. E. Martinez Legaz, J. Dutta, M. Lopez and other). This is one of the most advanced branches of abstract convexity.    I am also very interested in application of abstract convexity to theory of global optimization.

 7. What are the most interesting unsolved problems in the optimization branch you are working on:

 Theory of global optimization.   Local optimization theories are based on calculus and its nonsmooth generalizations.   Calculus is not suitable for investigation of global optima, so some new techniques should be invented.  Currently there are verified conditions for global optimum only for very narrow classes of problems, including convex problems.    I hope very much that some ideas and methods from abstract convexity can be successfully applied for description of verified conditions for   important classes of global optimization problems.        

 8. What kinds of topics excite your research interests?

 I am very exciting when I discover some links between different ideas in different fields.  When I invent a new perhaps awkward construction, which can be used for solution of some unsolved problems.    When I can give a new definition that sheds light on a complicated construction and allows one to look at this construction from a completely different point of view. When I can give a simple transparent proof of a complicated theorem based on a new definition.  When I can discover a new fact using a theory developed by myself.  

9. How did you develop these interests? What would you say is one of the most interesting topics you have studied?

  A wish and hope to understand what is really valid?   A wish and hope to show that the invented technique is useful.  Discussions with different experts, who can look at a problem in hand from a different point of view, are very important. 

 There are many interesting topics and it is difficult to say which of them are most interesting.   Perhaps, the turnpike theory in economic dynamics should be mentioned and supremal generators in abstract convexity. The theories mentioned in question 6 are very interesting. Of course my current research is the most interesting. Perhaps later on I will change my opinion. 

10.   When and how did you come to Ballarat?

 I am very thankful to Barney Glover, who invited me to Ballarat.

 Perhaps it is good to mention how it happened. In 1992 Barney sent a letter to Vladimir  Demyanov, my friend  from 1958 and my co-author, asking him some questions related to the book written by Vladimir and myself.   Since the questions were related to my part of the book, Vladimir sent this letter to me (I was in Baku from 1988.)  I prepared a reply and sent it to Barney.  No answer. Three months later I repeated this letter and this time Barney got it. He sent me a new letter and I replied again.  It took about two months for a letter to get Baku from Ballarat or to get Ballarat from Baku, so I had a reply for my letter in 4-5 months. It was very difficult to discuss some research problems if you got a reply on your question or your suggestion in 4 months.   In 1993 I was invited to visit Ankara and I got a regular access to e-mail there (first time in my life).  We had very interesting discussions with Barney by e-mail. As the result, a paper was prepared during this visit and then Barney invited me to visit Ballarat for two weeks in 1994.  During these two weeks a paper by myself, Barney and Jeya, describing some solvability theorems in terms of abstract convexity, was prepared.   We worked with Barney very successfully and in 1996 he invited me to apply for a post doc position at University of Ballarat.  I won a competition and became a post doc there.

 11. To round off the interview, what are some highlights of your career?

 I was very lucky to start my research carrier in Sobolev Institute of Mathematics in Novosibirsk. It was a strong team. We were young and energetic and a long life was before us.   And we had wise mentors including L. Kantorovich, who was a great mathematician and also won a Nobel Price in economics,

I am very lucky to have a position at University of Ballarat.  I like this small very friendly university.   We have a very strong optimization team here.

 My PhD students.   Supervision of PhD students is an important part of my research carrier, I like to explain a new problem to young people and share my ideas with them. I like their criticism and new ideas that can appear as the result of a fresh view on a problem. I supervised around 40 PhD students (some of them I supervised unofficially, since I have no right to supervise them formally in former SU).  Currently some of my former PhD students are known experts in optimization, economics and abstract convexity.

 My co-authors. I like to work with co-authors.  I wrote papers and books with more than 80 co-authors.  Young co-authors are similar to PhD students.  The work with an experienced co-author is quite different and very interesting and exciting.