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Linear Programming And Extensions. by George B. Dantzig

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1NPTEL Lectures: Mathematics - Linear Programming And Extensions

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Lectures from the National Programme on Technology Enhanced Learning - Mathematics - Linear programming and Extensions

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  • Title: ➤  NPTEL Lectures: Mathematics - Linear Programming And Extensions
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  • Language: English

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2DTIC AD0642276: AN ALGORITHM FOR SOLVING THE LINEAR INTEGER PROGRAMMING PROBLEM OVER A FINITE ADDITIVE GROUP, WITH EXTENSIONS TO SOLVING GENERAL LINEAR AND CERTAIN NONLINEAR INTEGER PROBLEMS

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Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general problem that lie in an optimal basis for the associated linear program. Gomory has shown how to solve the special knapsack problem by adapting a dynamic programming recursion originally designed for the ordinary knapsack problem, and has identified sufficient conditions under which the solution of the special knapsack problem will satisfy the nonnegativity requirements in the general integer program, thereby yielding an optimal solution to that problem as well. In this paper the author presents an algorithm for solving the special knapsack problem that is capable of accommodating a variety of constraints in addition to the special knapsack constraint. The purpose in doing this is to expand the range of problems for which the optimal solution for the special problem will also provide an optimal solution to the general integer program from which it was derived.

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  • Title: ➤  DTIC AD0642276: AN ALGORITHM FOR SOLVING THE LINEAR INTEGER PROGRAMMING PROBLEM OVER A FINITE ADDITIVE GROUP, WITH EXTENSIONS TO SOLVING GENERAL LINEAR AND CERTAIN NONLINEAR INTEGER PROBLEMS
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  • Language: English

“DTIC AD0642276: AN ALGORITHM FOR SOLVING THE LINEAR INTEGER PROGRAMMING PROBLEM OVER A FINITE ADDITIVE GROUP, WITH EXTENSIONS TO SOLVING GENERAL LINEAR AND CERTAIN NONLINEAR INTEGER PROBLEMS” Subjects and Themes:

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3DTIC AD0274596: A LINEAR PROGRAM OF PRAGER'S. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 60

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For the problem of minimizing the integral f(x)dx from limits of 0 to 1 subject to the constraints - f(x) xg(y) f(x) if 0 x y 1, - f(x) xg(y) - x + y f(x) if 0 y x 1, solutions are given to prove both that they satisfy the constraints and that they have the extremizing property. The problem arose in an elastico-plastic, structural-design context.

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  • Title: ➤  DTIC AD0274596: A LINEAR PROGRAM OF PRAGER'S. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 60
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4DTIC AD0263628: THE DECOMPOSITION ALGORITHM FOR LINEAR PROGRAMMING. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 57

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A procedure is presented for the efficient computational solution of linear programs having a certain structural property characteristic of a large class of problems of practical interest. This property makes possible the decomposition of the problem into a sequence of small linear programs whose iterate solutions solve the given problem through a generalization of the simple method for linear programming.

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5DTIC AD0263219: ON THE SOLUTION OF TWO-STAGE LINEAR PROGRAMS UNDER UNCERTAINTY. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 55

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A possible method for compensating for uncertainty in linear- programming problems is to replace the random elements by expected values or by pessimistic estimates of these values, or to recast the problem into a two-stage program so that, in the second stage, one can compensate for inaccuracies in the first stage. The purpose of this analysis is to examine the last of these methods in detail. More precisely, it investigates the conditions under which the first-stage decisions are optimal. In addition, formulas for using various existing computational algorithms to obtain an optimal solution are given.

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  • Title: ➤  DTIC AD0263219: ON THE SOLUTION OF TWO-STAGE LINEAR PROGRAMS UNDER UNCERTAINTY. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 55
  • Author: ➤  
  • Language: English

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6DTIC AD0297757: EXPERIMENTS IN LINEAR PROGRAMMING: NOTES ON LINEAR PROGRAMMING AND EXTENSIONS - PART 63

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A possible method for compensating for uncertainty in linear- programming problems is to replace the random elements by expected values or by pessimistic estimates of these values, or to recast the problem into a two-stage program so that, in the second stage, one can compensate for inaccuracies in the first stage. The purpose of this analysis is to examine the last of these methods in detail. More precisely, it investigates the conditions under which the first-stage decisions are optimal. In addition, formulas for using various existing computational algorithms to obtain an optimal solution are given.

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  • Title: ➤  DTIC AD0297757: EXPERIMENTS IN LINEAR PROGRAMMING: NOTES ON LINEAR PROGRAMMING AND EXTENSIONS - PART 63
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7DTIC AD0277519: SIMPLEX METHOD AND THEORY. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS - PART 62

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The simplex method of linear programming is discussed in a format designed to exhibit overall structure rather than specific operational details. Various terminal possibilities reprepresented schematically and geometrically, and it is shown that transposition duality theorems can be regarded as corollaries of the duality theorem for a homogeneous linear program.

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8Introduction To Linear Programming : Applications And Extensions

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The simplex method of linear programming is discussed in a format designed to exhibit overall structure rather than specific operational details. Various terminal possibilities reprepresented schematically and geometrically, and it is shown that transposition duality theorems can be regarded as corollaries of the duality theorem for a homogeneous linear program.

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  • Title: ➤  Introduction To Linear Programming : Applications And Extensions
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9Linear Programming And Extensions

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The simplex method of linear programming is discussed in a format designed to exhibit overall structure rather than specific operational details. Various terminal possibilities reprepresented schematically and geometrically, and it is shown that transposition duality theorems can be regarded as corollaries of the duality theorem for a homogeneous linear program.

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  • Title: ➤  Linear Programming And Extensions
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  • Language: English

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10DTIC AD0274595: LINEAR PROGRAMMING IN A MARKOV CHAIN. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 59

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An infinite Markov process with a finite number of states is considered in which the transition probabilities for each stage range independently over sets that either are finite or are convex polyhedra. A finite computational procedure is given for choosing those transition probabilities which minimize appropriate functions of the resulting equilibrium probabilities.

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  • Title: ➤  DTIC AD0274595: LINEAR PROGRAMMING IN A MARKOV CHAIN. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 59
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  • Language: English

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11Linear Programming And Extensions

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Bibliography: p. 592-610

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  • Language: English

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