Sunday 25 November 2018

Who First Conceived of Linear Programming and How did it Become Mainstream

Linear programming (LP) was first conceived in 1939 by Kantarovich, who began studies at Leningrad University (now known as the Saint Petersburg State University) at the age of 14.

He developed LP in the context of the real-world problem of optimizing production in the plywood industry.

(Quiz question - what was Kantarovich's middle name? Answer - Vitalievich).

Kantarovich published his findings in a 1939 book called "The Mathematical Method of Production Planning and Organization". He received the Nobel Prize as well as the Soviet Union's Lenin Prize (1965) and the Order of Lenin (1967), the highest civilian decoration bestowed by the Soviet Union.

Portland-Oregon born George Dantzig, whose parents were linguists (his father Tobias was also a mathematician) took Kantarovich's ideas further and developed an algorithm to address LP problems.

The so-called "simplex method" in 1948 made LP practical for use in solving real world problems. The name "simplex" refers to the shape of the search space for the feasible set.

The related theory of duality was later developed by John von Neumann.

Friday 23 November 2018

What Pythonistas Ought to Know About NEGs

Euclidean geometry (we will call it EG) is very familiar thanks to Euclid's Elements. EG possesses the interesting fact that the sum of the angles of a triangle at up to 180 degrees, or PI radians. This property is not shared by non Euclidean geometries (we shall call it NEGs) including spherical and hyperbolic geometries.