Researchers Discover the Optimal Way to Optimize
3 days ago
- #simplex-method
- #mathematics
- #optimization
- George Dantzig accidentally solved two famous open problems in statistics in 1939, which later inspired the film 'Good Will Hunting'.
- Dantzig invented the simplex method in the 1940s to solve optimization problems for the U.S. Air Force, which is still widely used today.
- The simplex method converts optimization problems into geometry problems, navigating complex polyhedrons to find the most efficient solutions.
- In 1972, mathematicians proved the simplex method could take exponentially longer in worst-case scenarios, raising theoretical concerns.
- Sophie Huiberts and Eleon Bach's 2023 paper improves the simplex method's efficiency and addresses theoretical concerns about exponential runtimes.
- Their work builds on a 2001 result by Daniel Spielman and Shang-Hua Teng, introducing randomness to avoid worst-case scenarios.
- The new research provides stronger mathematical support for the simplex method's practical efficiency, easing fears of exponential complexity.
- Future research aims to achieve linear scaling with constraints, though this remains a distant goal.