Technikatörténeti szemle 12. (1980-81)
TANULMÁNYOK - Filep László: A matematikai programozás kialakulása és fejlődése
7. Farkas Gyula: „Paraméteres módszer Fourier mechanikai elvéhez", Mathematikai és Physikai Lapok, 7. (1898.), 63—71. 8. Farkas, J.: „Theorie der einfachen Ungleichungen", Journal für die reine und angewandte Mathematik. 124. (1901.). 1—27. 9. Filep László: „Farkas Gyula élete és munkássága", Egyetemi doktori értekezés. Debrecen. 1977. 10. Gale, D.— Kuhn, H. W.—Tucker, A. W.: Linear programming and the theory of games. (15)-ben. 317—329. 11. Gomory, R. E.: „An algorithm for integer solutions to linear programs", Princeton — IBM Math. Res. Project. Techn. Rep. No. 1. (1958.). 12. Haar Alfréd: „A lineáris egyenlőtlenségekről", Mathematikai és Természettudományi Értesítő, 36. (1918.). 279—296. 13. Hitchock, F. L.: „Distribution of a Product from Several Sources to Numerous Localities", J. Math. Phys. 20. (1941.). 224—230. 14. Kantorovics, L. V.: „Mathematyicseszkije metodi organizacii i planyirovanyija proizvodsztvo", Izd. LGU. Leningrád, 1939. 15. Koopmans, T. C: ..Activity Analysis of Production and Allocation", Wiley, New York (1951.). 16. König Dénes: „Graphok és Mátrixok", Matematikai és Fizikai Lapok, 39. (1931.). 17. Kuhn, H. W.: „The Hungarian Method for Solving the Assignment Problem", Naval Research Logistics Quarterly, 1955. Vol. 2. 83. 18. Kuhn, H. W. —Tucker, A. W.: „Nonlinear programming", Proceedings of the Second Berkeley Symposium on Math. Stat, and Probab. Berkeley. 1950. 481—492. 19. Martos Béla: „Hiperbolikus programozás", MTA Matematikai Kutatóintézet Közleményei, 1960. 20. Neumann, J.:— Morgenstern, O.: „Theory of Games and Economic Behavior", Princeton, 1944. L. FILEP: BIRTH AND DEVELOPMENT OF MATHEMATICAL PROGRAMMING The mathematical programming (the optimization theory) is a relatively new branch of mathematics. Its task is to find the maximum or minimum of an objective function, subject to certain constraints. It can be regarded as a part of operations research too. First the linear programming and the game theory were developed. Kantorovics elaborated the method of solving coefficients in 1939 (14), Hitchock solved the transportation problem in 1941 (13). The founder of game theory was János Neumann. Ábrahám Wald was the first, who enriched the theory. (Both Neumann and Wald were Hungarian by birth). The linear programming and the game theory were employed in military science during the second world war, and in economics after the war. Methods for solving the problems of linear programming were elaborated: the simplex method by Dantzig in 1951, the Hungarian method — based on a theorem of Dénes Kőnig and Jenő Egerváry (3,16) — by Kuhn in 1955. In 1947 János Neumann based the duality theory and showed that the general linear programming problem is equivalent to a two-person zero-sum game. Gyula Farkas' and Alfréd Haar's some results published formerly have proved of fundamental importance in the theory of linear programming. These results are: the Farkas-theorem (5,8), the Haar-theorem (12). The development of nonlinear programming started with the paper (18), where the fundamental theorem of mathematical programming was proved. Since then several branches of nonliear programming have evolved, such as convex programming, quadratic programming, hyperbolic programming (Béla Martos, 1960), dynamic programming (Bellmann, 1957), stochastic programming, and integer programming.
