“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.

George B. DantzigAge: 25

Jerzy NeymanProfessor of Statistics

ad

vis

or

not the same personThesis 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.”

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)

A General linear program.

The Simplex Method.

Every constraint specifies ann-dimensional half-space.

Travel along “edges” untilno 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

1949. The University of Chicago.

The Zero Symposium

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 thatthe simplex method could takeexponentially many steps to solve anLP in the worst case…

Is there aprovablyefficient

algorithm?

The cold war.

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…”

2004. A strongly polynomial algorithm?