The Basic George B. DantzigStanford University Press, 2003 - 378 pàgines The late George B. Dantzig , widely known as the father of linear programming, was a major influence in mathematics, operations research, and economics. As Professor Emeritus at Stanford University, he continued his decades of research on linear programming and related subjects. Dantzig was awarded eight honorary doctorates, the National Medal of Science, and the John von Neumann Theory Prize from the Institute for Operations Research and the Management Sciences. The 24 chapters of this volume highlight the amazing breadth and enduring influence of Dantzig's research. Short, non-technical summaries at the opening of each major section introduce a specific research area and discuss the current significance of Dantzig's work in that field. Among the topics covered are mathematical statistics, the Simplex Method of linear programming, economic modeling, network optimization, and nonlinear programming. The book also includes a complete bibliography of Dantzig's writings. |
Continguts
Mathematical Statistics | 1 |
The Simplex Method of Linear Programming | 19 |
The generalized simplex method for minimizing a linear | 33 |
LargeScale Linear Programming | 45 |
Decomposition principle for linear programs | 61 |
Generalized upper bounding techniques | 72 |
Special Applications and Economic Modeling | 89 |
A linear programming approach to the chemical equilibrium | 98 |
Multistage stochastic linear programs for portfolio | 180 |
Network Optimization | 201 |
On the maxflow mincut theorem of networks | 225 |
On the shortest route through a network | 232 |
Integer Linear Programming and Linear Inequalities | 237 |
FourierMotzkin elimination and its dual | 255 |
On the continuity of the minimum set of a continuous | 276 |
Complementarity Problems | 305 |
Frases i termes més freqüents
affine functions apply approximation assume b₁ basic feasible solution basic solution basic variables basis block triangular Chapter chemical equilibrium coefficients columns complementary components computational constraints convex function convex set corresponding costs decomposition defined demand function denote dual EC(b equations equilibrium example exists expected extreme point finite Fulkerson G.B. Dantzig GEORGE George Dantzig given H(tn H(to Hence importance sampling income integer inverse iteration Lemma linear complementarity problem linear inequalities linear programming problem Math Mathematical Programming matrix maximal minimizing multi-stage nodes Nonlinear Programming nonnegative objective function obtained Operations Research optimal solution paper parameters period positive procedure PROOF quadratic programming RAND Corporation random satisfying scenario wt sequence simplex algorithm simplex method solving stage stochastic programming subset Suppose technique Theorem theory tour two-stage upper bound utility function vector x₁ zero