Karmarkar's breakthrough

Karmarkar's breakthrough was a new method developed in 1984 for solving large-scale optimization problems more efficiently. Unlike earlier techniques, his algorithm could find optimal solutions faster and use less computational resources, especially for complex problems with many variables. This advancement significantly improved the ability of computers to handle large, real-world challenges in fields like logistics, finance, and engineering. Karmarkar's work introduced a powerful new approach called interior-point methods, which navigate the problem's feasible region from within, rather than along its edges, leading to a leap forward in optimization mathematics.