“for the most part even to this day, a great gulf exists between man’s aspirations and his...
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“For the most part even to this day, a great gulf exists between man’s aspirations and his actions.” -- George B. Dantzig
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1939. University of California, Berkeley.
George B. DantzigAge: 25
Jerzy NeymanProfessor of Statistics
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vis
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not the same personThesis on Lagrange multipliers (i.e. duality)
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1941. The Pentagon, Washington.
1941-1946: Dantzig works for the US government developing methods for logistical and operational planning… (using desk calculators)
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1946. USS Air Force, Washington.
“Non-computability was the chief reason, I believe, for a total lack of interest in optimization prior to 1947.”
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.
Air Force intiated SCOOP (Scientific Computing of Optimum Programs)
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A General linear program.
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The Simplex Method.
Every constraint specifies ann-dimensional half-space.
Travel along “edges” untilno improvement can be made.
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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
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1949. The University of Chicago.
The Zero Symposium
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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.”
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But what will the theorists do?
In 1970, Klee and Minty showed thatthe simplex method could takeexponentially many steps to solve anLP in the worst case…
Is there aprovablyefficient
algorithm?
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The cold war.
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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…”
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2004. A strongly polynomial algorithm?