Methods of Mathematical Economics: Linear and Nonlinear Programming, Fixed-Point Theorems
Many advances have taken place in the field of combinatorial algorithms since Methods of Mathematical Economics first appeared two decades ago. Despite these advances and the development of new computing methods, several basic theories and methods remain important today for understanding mathematical programming and fixed-point theorems. In this easy-to-read classic, readers learn Wolfe's method, which remains useful for quadratic programming, and the Kuhn-Tucker theory, which underlies quadratic programming and most other nonlinear programming methods. In addition, the author presents multiobjective linear programming, which is being applied in environmental engineering and the social sciences. The book presents many useful applications to other branches of mathematics and to economics, and it contains many exercises and examples. The advanced mathematical results are proved clearly and completely.
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algorithm assume assumption Banach space barycentric coordinates barycentric subdivision basic cones basic feasible solution basic solution basis matrix boundary Brouwer fixed-point theorem Brouwer theorem called canonical minimum problem cell coefficients compute concave condition continuous function convergent convex set cost vector cºx criterion row current basis define differentiable dimensions dual equations dual vector equals equilibrium theorem example Figure finite number fixed point formula gives implies inequality lemma linear programming look lower bound mapping mathematics maximal flow maximum minimize mixed strategy non-basic non-degenerate non-zero optimal real solution payoff matrix perturbation Phase pivot column pivot row player positive components posynomial proof prove pure strategies quadratic program require satisfy sequence sign constraints simplex algorithm simplex method solves MAX Sperner's lemma subset Suppose tangents theorem says theory unique unit ball unit vectors variables write zero