George Dantzig

George Dantzig (1914–2005) was an American mathematician who developed the simplex algorithm for linear programming and helped establish operations research as a discipline.

Leonid Kantorovich: A Soviet mathematician and economist who developed mathematical methods for optimizing resource allocation. His independent work on linear programming paralleled Dantzig’s and later shared the 1975 Nobel Memorial Prize in Economic Sciences.
Simplex algorithm: An iterative method for optimizing a linear objective over a polyhedron by moving between its vertices. Dantzig devised this algorithm to solve linear programs efficiently in practice.
Operations research: The use of mathematical models and analytical methods to support decisions in complex systems. Dantzig helped turn wartime operations analysis into a broader mathematical discipline.
United States Air Force: The aerial warfare service branch of the United States armed forces, established as an independent service in 1947. Dantzig developed optimization methods while working on military planning problems during World War II.
Dantzig–Wolfe decomposition: A method that decomposes a large linear program into a master problem and smaller subproblems. Dantzig and Philip Wolfe developed it to exploit structure in large optimization problems.
John von Neumann: A mathematician whose work shaped game theory, computing, and mathematical economics. He recognized the significance of Dantzig’s linear-programming work and connected it to duality and game theory.
Reduced cost: A quantity in linear programming that measures how an objective changes when a nonbasic variable enters a solution. The simplex method uses reduced costs to identify promising moves toward a better solution.
Diet problem: A linear-programming problem that finds the least-cost combination of foods meeting specified nutritional requirements. Its formulation helped demonstrate how linear programming could solve practical allocation problems.
World War II: A global war fought from 1939 to 1945 between the Axis powers and the Allies. Wartime demands for coordinated planning created problems that motivated Dantzig’s early operations-research work.
Linear programming: A method for optimizing a linear objective subject to linear equality and inequality constraints. Dantzig’s algorithm made this framework broadly usable, though this page links to it under mechanism.

Linked from 6 pages