Advanced Modeling and Optimization

Obituary


Ilya I. Dikin (1936 - 2008)

Ilya I. Dikin, a member of the editorial board of the Electronic International Journal Advanced Modeling and Optimization, died unexpectedly on February 28, 2008, at the age of 71.

I. Dikin obtained his diploma in mathematics at Tomsk State University. In 1963-1966 he was a post-graduate student at the department of computational mathematics at Novosibirsk State University under the supervision of academician L.V. Kantorovich (a Nobel prize-winner of 1975). Then I. Dikin worked in Novosibirsk: at the Research Institute of Systems and then at the Institute of Applied Physics; in Irkutsk: first at the Computational Center at State University and then from 1971 and till the end of his life at Energy Systems Institute, SB RAS (former Siberian Energy Institute, SB AS of the USSR). I. Dikin received his PhD degree in mathematics in 1973.

I. Dikin came to Energy Systems Institute as a mature researcher and became one of the leading specialists in the field of optimization theory and methods. He is the author of an original method for solving mathematical programming problems – the method of interior points. He managed to obtain a series of results on the convergence of the proposed algorithms. I. Dikin devoted much of his effort and energy to putting the method into practice for calculation of optimization problems. The efficient algorithms of search for feasible and optimal solutions proposed by him have been implemented in computational programs to solve the problems in various fields of energy including optimization and control problems of electric power system operation, the problems of power system reliability, the problems of fuel supply optimization; in equilibrium thermodynamics; in calculations of flow distribution in hydraulic systems, etc. Besides, I. Dikin dealt with the analysis of the continuous gradient process of determining a saddle point of the Lagrange function and its generalizations, and the analysis of continuous processes put in correspondence with the problems of linear and nonlinear complementarity.

I. Dikin is the author of about 100 research papers (including 4 monographs). Many of them were published in prestigious Russian and International journals. His works received international recognition and were presented by him at international mathematical symposia. His method for improving feasible solutions was named the affine scaling method. It spawned a whole new branch of research dealing with the internal point algorithms. I. Dikin is highly respected by his colleagues in Russia and abroad. His publications have high citation index. He is renowned for great scientific erudition and consistency. Adherence to his principles and amicability earned him the well-deserved respect.

I. Dikin went to Lake Baikal every year (both as a participant of scientific workshops and conferences and as a vacationer) and was an active participant in the Baikal protection campaigns.

Ilya was dedicated to his work, family, and friends. He was a good friend I will miss.

Olga Popova
Energy Systems Institute, Lermontova 130, 664033 Irkutsk, Russia.
June 16, 2008.



List of Selected Publications of Ilya I. Dikin

  • Iterative solution of linear and quadratic programming problems // Doklad AN SSSR. – 1967. – Vol. 174, No. 4. – Pp. 747-748. (in Russian)
  • On continuous analogs of the interior points method // Controlled systems. Novosibirsk: IM SO AN SSSR, 1971. – Issue 9. – Pp. 59-64. (in Russian)
  • On convergence of an iterative process // Controlled systems. – Novosibirsk: IM SO AN SSSR, 1974. – Issue 12. – Pp. 54-60.
  • Study of optimal programming problems by the interior points method // Optimization methods. – Irkutsk: SEI SO AN SSSR, 1975. – Pp. 72-108. (in Russian)
  • Determination of the relatively interior point of the system of inequality and equality constraints // Controlled systems. Discrete extremal problems. – Novosibirsk: IM SO AN SSSR, 1978. – Issue 17. – Pp. 60-66. (in Russian)
  • The interior points method in mathematical programming // Applied mathematics. – Novosibirk: Nauka. Sib. otd-nie, 1978. – Pp. 139-158.
  • Determination of the interior point of a system of linear inequalities // Kibernetika i sistemnyi analiz. – 1992. – No. 1. – Pp. 67-74. (in Russian)
  • The interior points method in linear programming // Optimization: models, methods, solutions. – Novosibirsk: Nauka. Sib. otd-nie, 1992. – Pp. 54-69. (in Russian)
  • Determination of the interior feasible point of the system of linear constraints // Kibernetika i sistemnyi analiz. – 1997. – No. 5. – Pp. 152-164. (in Russian)
  • Continuous variants of the interior points method // Association of mathematical programming. – Ekaterinburg, 2001. – Informatsionnyi byulleten No. 9. – Pp. 38-41. (in Russian)
  • Convergence of a dual-variable vectors sequence in a semi-definite programming problem // Cybernetics and Systems Analysis. – 2003. – Vol. 39, No. 2.
  • Solution of systems of equalities and inequalities by the method of interior points // Cybernetics and Systems Analysis. – 2004. – Vol. 40, No. 4. – P p. 625-628.
  • Solution of a problem of geometric programming // Cybernetics and Systems Analysis. – 2005. – Vol. 41, No. 6. – P p. 936 – 939.
  • Examples in the theory of convergence of the affine scaling method // Cybernetics and Systems Analysis. – 2006. – Vol. 42, No. 1 – Pp. 157 – 158.
  • Letter to the editor // Mathematical programming. – 1988. – Vol. 41, No. 3. – Pp. 393-394.
  • Determination of internal feasible point // Proc. 13 th Intern. Symp. on Mathematical programming: Abstracts. – Tokyo, 1988. – P. 230.
  • Affine scaling methods for linear programming // Research Memorandum, No 479. − Tokyo: Institute of Statistical Mathematics, 1993. − 24 p.
  • Convergence of the dual variables for the primal affine scaling method with unit steps in the homogeneous case // J. Optimization Theory and Applications. − 1997. − Vol. 95, No. 2. − Pp. 305-321. (Co-author Roos C.)
  • In the book: George B. Dantzig, Mukund N. Thapa. Linear Programming 2: Theory and Extensions (Springer Verlag New York, 2003), in Chapter 3 “Early interior-point methods”, Paragraph 3.2 “Dikin’s method”.

 

Dr. I. Dikin’s monographs:

  • Iterative solution of mathematical programming problems: algorithms of the interior point method. – Novosibirsk: Nauka. Sib. otd-nie, 1980. – 144 p. (Co-author Zorkaltsev B.I.). (in Russian)
  • Study and acceleration of convergence of the algorithms for the interior point method: Solution to optimization problems of thermodynamics. – Novosibirsk: Nauka. Sib. predpriyatie RAN, 1997. – 70 p. (Co-author Popova O.M.) (in Russian)
  • Determination of feasible and optimal solutions by the interior point method. – Novosibirsk: Nauka. Sib. predpriyatie RAN, 1998. – 110 p. (in Russian)
  • The interior point method in linear and nonlinear programming. – Novosibirsk: Nauka. Sib. predpriyatie RAN, 2008. – 104 p. (to be published). (in Russian)

 

Published in the AMO journal:

  • Determination of interior points of systems of inequality and equality constraints // Advanced Modeling and Optimization. − 1999. − Vol. 1, No. 1. − Pp. 1-8.
  • Acceleration of the affine scaling method convergence for optimization problems of thermodynamics // Advanced Modeling and Optimization. − 1999. − Vol. 1, No. 3. − Pp. 30-44. (Co-author Popova O.M.).
  • On construction of the asymptotic stability region on the plane // Advanced modeling and optimization. − 2001. − Vol. 3, No. 2. − Pp. 1-5. (Co-author Popova O.M.).

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