Why was Narendra Karmarkar’s interior point method important for solving linear programming problems?

Narendra Karmarkar’s interior point method was a significant breakthrough in linear programming because it provided a polynomial-time algorithm that was practically efficient.1

While the simplex method, introduced by George Dantzig, was the standard for solving linear programming problems, it faced limitations as problem complexity increased; the number of operations required could grow exponentially, exceeding the capacity of even powerful computers.1

Although the ellipsoid method discovered by Leonid Khachiyan in 1979 was the first to offer a polynomial-time solution, it proved slower than the simplex method in practical applications. Karmarkar’s 1984 discovery of the interior point method was important because it combined the theoretical efficiency of a polynomial-time algorithm with a speed that made it truly competitive with the simplex method for solving complex, large-scale problems.1