L.V.Kantorovich and Linear Programming

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📝 Original Info

  • Title: L.V.Kantorovich and Linear Programming
  • ArXiv ID: 0707.0491
  • Date: 2007-07-05
  • Authors: ** 작성자 미상 (본 텍스트는 회고록·기록 형태로, 명시된 저자 정보가 제공되지 않음) **

📝 Abstract

I want to write about what I know and remember about the activities of Leonid Vital'evich Kantorovich, an outstanding scientist of the 20th century; about his dramatic struggle for recognition of his mathematical economic theories; about the initial stage of the history of linear programming; about beautuful Kantorovich metric, about the creation of a new area of mathematical activity related to economic applications, which is called sometimes operation research, sometimes mathematical economics, sometimes linear and convex programming, or economic cybernetics, etc.; about its place in the modern mathematical landscape; and, finally, about several personal impressions of this distinguished scientist. The notes in no way pretend to exhaust these topics.

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known reasons, people with "flawed" biographies could find a job at civil enterprises (such as the Egorov Plant). Sometimes this resulted in the professional level at such a plant being above the average. For the same reasons, G.Sh. (patronized by L.V.) managed to get a job at the Kirov Plant, where he also tried to introduce optimization methods and simply reasonable approaches to problems of local planning. Note that G.Sh. graduated from the university at the time when he, being a veteran of the war and a successful student, could not enter a graduate school. Before the war, G.Sh. studied at the Odessa University and was a student of M. G. Krein, so that he successfully combined the knowledge of that part of the work of M. G. Krein and the whole Ukrainian school of functional analysis that was close to L.V.'s activities (the L-moment problem) with the good understanding of L.V.'s ideas in linear programming. There were also attempts to introduce optimization methods at the Skorokhod Factory, Lianozovo (ex-Egorov) Wagon Plant, Kolomna Locomotive Plant, etc. But, amazingly, this activity met the resistance of those who would seem to be most interested in it. At the time, as well as later, there existed a number of comical examples of reasons why some or another well-founded suggestion did not find support. For instance, suggestions on optimal cutting came into conflict with the bonus promised to those who collected more waste products for recycling, etc. Afterwards, optimal cutting was much studied by the Novosibirsk pupils of L.V., in particular, E. A. Mukhacheva.

Were there any serious reasons why this useful activity met such difficulties and was not on demand at the time? All of the few papers on this subject written at those “underground” years were meant for engineers and published in nonmathematical editions available for engineers. It would seem to be the best example of “cooperation of science and industry,” which opened wide horizons for scientific, mathematically-based, local and global planning in economics. At the early period (1939)(1940)(1941)(1942)(1943)(1944)(1945)(1946)(1947)(1948)(1949), one might think that the reason of this antagonism was in the unpreparedness of people and their working conditions to comprehend these ideas and techniques, as well as in the deathening ideological dogmata and stupidity of the Party supervisors and ideologists. One might think that if the authorities were more enlightened, they would be able to appreciate, implement, and use the new ideas. Perhaps, L.V. also thought so. But the entire subsequent Soviet history showed that the situation was much worse. . . At the time, and even later, it was not thoroughly understood that the reason behind the failure of implementing the most part of new economic (and other) ideas was not in particular circumstances or in the stupidity of bureaucrats, but in the fact that the whole Soviet economic system, or, as it was called later, command-administrative system, is organically unable to accept any innovations, and no serious, big or small, economic reforms leading to stability just cannot be realized inside it.

It was not until the middle of 1956 that L.V. started actively promoting this subject and giving lectures at the Department of Mathematics and Mechanics and other departments of the Leningrad University, at the Leningrad Department of the Steklov Institute of Mathematics (LOMI). This was the disclosure of a new, earlier forbidden, area. He told about the contents of his 1939 book, about resolving multipliers, various models and problems, etc. For the overwhelming majority of the audience, including myself, these topics were completely, or almost completely, new. Undoubtedly, the “declassification” of this subject had to do with the new hopes appeared after Stalin’s death, Khrushchev’s speech, and the beginning of the “Thaw.” At this point, it is pertinent to recall V. I. Arnold’s story about A. N. Kolmogorov: being asked by V.I. why in 1953-1954 A.N. suddenly started working on the classical and very difficult problem of small denominators (this was the beginning of what is now called KAM theory), on which he had never worked before, A.N. answered: “Some hope has emerged.”

Undoubtedly, some hope had emerged also for L.V., the hope that he would finally be able to explain and implement his ideas and to overcome the Soviet dogmatism and obscurantism in economics.

When one says that the Soviet science (not the whole science, but, say, mathematics) was successfully developing and reached a very high level, there is no arguing, but one still must not forget about this and many other similar stories: ideological pressure, selection according to personal details, etc. never allowed a gifted man to realize his talent in full measure or even did not allow to realize it at all. The indubitable scientific achievements of the Soviet period is only a small part of what could appear in the conditions of freedom, and the los

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