Methods of Mathematical Economics: Linear and Nonlinear Programming, Fixed-point Theorems

Joel N. Franklin

Jan 1980 · Classics in Applied Mathematics Kitabu cha 37 · SIAM

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Linear programming. Introduction to linear programming -- Linear programs and their duals -- How the dual indicates optimality -- Basic solutions -- The idea of the simplex methods -- Separating planes for convex sets -- Finite cones and the Farkas alternative -- The duality principle -- Perturbations and parametric programming -- The simplex tableau algorithm -- The revised simplex algorithm -- A simplex algorithm for degenerate problems -- Multiobjective linear programming -- Zero-sum, two-person games -- Integer programming: Gomory's method -- Network flows -- Assignment and shortest-route problems -- The transportation problem -- Nonlinear programming. Wolfe's method for quadratic programming -- Kuhn-Tucker theory -- Geometric programming -- Fixed-point theorems. Introduction to fixed points -- Contraction mappings -- Garsia's proof of the Brouwer fixed-point theorem -- Milnor's proof of the Brouwer fixed-point theorem -- Barycentric coordinates, Sperner's lemma, and an elementary proof of the Brouwer fixed-point theorem -- The Schauder fixed-point theorem -- Kakutani's fixed-point theorem and Nash's theorem for n-person games.