The basic concepts of Interior Point Methods (IPMs) were introduced by Frish in 1950’s, and further developed in the 1960’s, among others by Fiacco-McCormick (SUMT) and Dikin (Affince scaling). By the early 70’s it was concluded that, mostly due to numerical instability, IPMs most probably will not be viable algorithms for solving large scale optimization problems.
Karmarkar’s 1984 paper and the subsequent “Interior Point Revolution” fundamentally changed the landscape of optimization. IPMs become the method of choice to solve large-scale linear optimization problems, new classes of conic and convex optimization problems become efficiently solvable. The new powerful algorithmic and software tools opened new areas of applications. In this talk we walk through the history of IPMs, highlight the scientific and computer technology advances that make the Interior Point revolution possible.