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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. 1939. University of California, Berkeley. advisor. George B. Dantzig. Jerzy Neyman. Age: 25. Professor of Statistics. not the same person.

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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


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)


1941. The Pentagon, Washington.

1941-1946:

Dantzig works for the US government developing

methods for logistical and operational planning…

(using desk calculators)


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.



The Simplex Method.

Every constraint specifies an

n-dimensional half-space.

Travel along “edges” until

no improvement can be made.


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



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.”


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?



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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