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Optimization Pioneer: George Dantzig's Legacy in Linear Programming

Explore the life and work of George Dantzig, the pioneering mathematician behind the simplex method in linear programming. Learn about his contributions, from wartime logistics planning to Cold War algorithms, shaping mathematical optimization. Discover the evolution of computational methods from desk calculators to modern algorithms. Delve into Dantzig's impact on theoretical and practical applications of linear programming.

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Optimization Pioneer: George Dantzig's Legacy in Linear Programming

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  1. “For the most part even to this day, a great gulf exists between man’s aspirations and his actions.” -- George B. Dantzig

  2. 1939. University of California, Berkeley. advisor George B. Dantzig Jerzy Neyman Age: 25 Professor of Statistics not the same person Thesis on Lagrange multipliers (i.e. duality)

  3. 1941. The Pentagon, Washington. 1941-1946: Dantzig works for the US government developing methods for logistical and operational planning… (using desk calculators)

  4. 1946. USS Air Force, Washington. “Non-computability was the chief reason, I believe, for a total lack of interest in optimization prior to 1947.” Air Force intiated SCOOP (Scientific Computing of Optimum Programs) Danzig formulated a formal model for “planning” problems: Solving a linear objective function subject to linear constraints. Invented the simplex method for finding optimal solutions to “linear programs” in a bounded number of steps.

  5. A General linear program.

  6. The Simplex Method. Every constraint specifies an n-dimensional half-space. Travel along “edges” until no improvement can be made.

  7. 1947. Institute for Advanced Study, Princeton. “Then, for the next hour and a half, he proceeded to give me a lecture on the mathematical theory of linear programs.” -- Dantzig about von Neumann

  8. 1949. The University of Chicago. The Zero Symposium

  9. A rapidly changing world. “It has been argued that (before pornography invaded the internet) the majority of CPU time used by computers world wide was devoted to running the simplex algorithm.”

  10. But what will the theorists do? In 1970, Klee and Minty showed that the simplex method could take exponentially many steps to solve an LP in the worst case… Is there a provably efficient algorithm?

  11. The cold war.

  12. 1979. Khachiyan proves that Linear Programming is in P. “Despite the assumed mediocrity of Soviet hardware, they could win the cold war, economically and militarily, if they had superior mathematical algorithms…”

  13. 2004. A strongly polynomial algorithm?

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