Farkas' lemma
Lema de Farkas
- Date
- 1902 · confidence high
- Place
- Cluj-Napoca, Cluj, Romania
- Credited to
- Gyula Farkas
- Field
- Knowledge & symbols
What was discovered
A theorem on the solvability of systems of linear inequalities: either the system has a solution or there is a certificate that it has none. Gyula Farkas published it while a professor at Kolozsvár.
Farkas taught at the University of Kolozsvár (now Cluj-Napoca, Romania). The result appeared in the Journal für die reine und angewandte Mathematik in 1902; Fourier had already worked on linear inequalities in 1826.
What it led to
- duality in linear programming (Dantzig, von Neumann, 1947-1950)
- Karush–Kuhn–Tucker optimality conditions
- game theory and mathematical economics