Linear programming develops practical techniques for optimizing linear functions on sets defined by systems of linear inequalities. Because many mathematical models in the physical and social sciences are expressed by such systems, the techniques developed in linear programming are very useful. This course will present the mathematics behind linear programming and related subjects. Topics covered may include the following: the simplex method, duality in linear programming, interior-point methods, two-person games, some integer-programming problems, Wolfe's method in quadratic programming, the Kuhn-Tucker conditions, and geometric programming. |