Dantzig, George B.Overview
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Most widely held works by
George B Dantzig
Linear programming and extensions
by George B Dantzig
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Book
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27 editions published between 1963 and 1998 in English and Undetermined and held by 86 WorldCat member libraries worldwide The linear programming concept; Origins and influences; Formulating a linear programming model; Linear equation and inequality systems; The simplex method; Proof of the simplex algorithm and the duality theorem; The geometry of linear programs; Pivoting, vector spaces, matrices, and inverses; The simplex method using multipliers; Finiteness of the simplex method under perturbation; Variants of the simplex algorithm; The price concept in linear programming; Games and linear programs; The classical transportation problem; Optimal assignment and other distribution problems; The transshipment problem; Networks and the transshipment problem; Variables with upper bounds; Maximal flows in networks; The primaldual method for transportation problems; The weighted distribution problem; Programs with variable coefficients; A decomposition principle for linear programs; Convex programming; Uncertainty; Discrete variable extremum problems; Stigler's nutrition model: an example of formulation and solution; The allocation of aircraft to routes under uncertain demand
Linear programming
by George B Dantzig
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Book
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1 edition published in 1997 in English and held by 23 WorldCat member libraries worldwide This combined book and software package contains worked examples and exercises for students to try out the methods covered and to develop a good working skill in this topic
Activity analysis of production and allocation : proceedings of a conference
by Yale University
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Book
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2 editions published in 1951 in English and held by 16 WorldCat member libraries worldwide
Mathematical Programming Essays in Honor of George B. Dantzig Part I
by Richard Cottle
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Book
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1 edition published in 1985 in English and held by 11 WorldCat member libraries worldwide
Mathematical Programming Essays in Honor of George B. Dantzig Part II
by Richard Cottle
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Book
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1 edition published in 1985 in English and held by 11 WorldCat member libraries worldwide
Mathematics of the decision sciences
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Book
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4 editions published between 1968 and 1970 in English and Undetermined and held by 10 WorldCat member libraries worldwide
Drews institutionalized divvy economy
by George B Dantzig
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Book
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3 editions published between 1973 and 1974 in English and held by 5 WorldCat member libraries worldwide
Largescale linear programming : Proceedings
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Book
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3 editions published in 1981 in Undetermined and held by 5 WorldCat member libraries worldwide
Largescale linear programming : proceedings of a IIASA workshop, 26 June 1980
by George B Dantzig
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Book
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2 editions published in 1981 in English and held by 4 WorldCat member libraries worldwide
The basic George B. Dantzig
by George B Dantzig
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Book
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2 editions published in 2003 in English and held by 4 WorldCat member libraries worldwide "George B. Dantzig, widely known as the father of linear programming, has been a major influence in mathematics, operations research, and economics. The 24 chapters of this volume highlight the amazing breadth and enduring influence of Dantzig's research. Short, nontechnical summaries at the opening of each part of the book 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."BOOK JACKET
Linear programming
by George B Dantzig
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Book
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2 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the simplex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in the first volume. It also includes additional advanced topics such as variants of the simplex method; interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will find this volume of particular interest
A complementarity algorithm for an optimal capital path with invariant proportions
by George B Dantzig
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Book
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2 editions published between 1973 and 1974 in English and held by 3 WorldCat member libraries worldwide
Expected number of steps of the simplex method for a linear program with a convexity constraint
by Stanford University
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Book
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3 editions published between 1980 and 1981 in English and held by 3 WorldCat member libraries worldwide When there is a convexity constraint, (Sigma)(lambda sub j) = 1, each iteration t of the simplex method provides a value z sub t for the objective and also a lower bound z sub t to w sub t. The paper studies (1) the expected behavior of (w sub t/w sub 0); (2) probability of termination on the t to th iteration; and (3) the expected number of steps, xi ITER, when the columns are drawn from a distribution from a three parameter class of distributions
Discovering Hidden Totally Leontief Substitution Systems
by Stanford University
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Book
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3 editions published in 1977 in English and held by 3 WorldCat member libraries worldwide A constructive procedure is given for determining the existence of and evaluating (when it does exist) a nonsingular matrix that transforms a system of linear equations in nonnegative variables into a totally Leontief substitution system. The computational effort involved is about that required to optimize the given mrow linear system with m+1 different linear objective functions. (Author)
COMPLEMENTARY SPANNING TREES
by George B Dantzig
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Book
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2 editions published in 1969 in English and held by 3 WorldCat member libraries worldwide Given a network G whose arcs partition into nonoverlapping 'clubs' (sets) R sub i, D. Ray Fulkerson has considered the problem of constructing a spanning tree such that no two of its arcs belong to (represent) the same club and has stated necessary and sufficient conditions for such trees to exist. When each club R sub i consists of exactly two arcs, we shall refer to each of the arc pair as the 'complement' of the other, and the representative tree as a complementary tree. Our objective is to prove the following theorem: If there exists one complementary tree, there exists at least two. (Author)
Comments on Khachian's Algorithm for Linear Programming
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Book
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1 edition published in 1979 in English and held by 2 WorldCat member libraries worldwide Khachian's polynomial bound for finding a feasible solution to a relaxed linear program is an important theoretical result. Unfortunately, a polynomial bound does not imply a good algorithm because such a bound could be too large for problems of practical interest. For example, using the formulae in the original paper, practical problems with 3000 nonnegative variables and 1000 equations (which are solved under onehalf hour on IBM 370168 using the simplex method) would involve over 10 to 15th power iterations and would take 50,000,000 years to solve using Khachian's method
Applications et prolongements de la programmation lineaire
by George B Dantzig
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Book
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2 editions published between 1966 and 1968 in French and held by 2 WorldCat member libraries worldwide
Theory and extensions
by George B Dantzig
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Book
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in English and held by 2 WorldCat member libraries worldwide
Symmetric dual nonlinear programs
by George B Dantzig
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Book
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1 edition published in 1962 in Undetermined and held by 2 WorldCat member libraries worldwide
Maximum diameter of abstract polytopes
by Stanford University
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Book
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2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide Walkup and Klee studied the diameter of ordinary convex polytopes which is defined as the smallest integer k such that all pairs of vertices can be joined by a path of k or less neighboring vertices. The well known dstep (or Hirsch) conjecture for d dimensional polytopes with n facets states that the maximum diameter is n  d. Walkup and Klee showed the conjecture as correct for all n  d <or = 5. In an effort to extend the results, the authors of the paper abstract (in the form of three simple axioms) some of the combinatorial properties of ordinary polytopes and show that these are sufficient to establish the maximum diameter is n  d for all n  d <or = 5 and a variety of bounds for other values of n and d. Abstract polytopes are a special class of pseudo manifolds. The results provide insight into the number of iterations required to solve a linear program using the simplex method. (Author) more
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Capital investmentsMathematical models Computer science Dantzig, George B.(George Bernard), Distribution (Economic theory) Economics Economics, Mathematical Industrial engineering Industrial priorities Industries Large scale systems Linear complementarity problem Linear programming Mathematical models Mathematical optimization Mathematical statistics Mathematics Operations research Production (Economic theory) Production functions (Economic theory) Production planning Programming (Mathematics)

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