This link has been bookmarked by 61 people . It was first bookmarked on 08 Jul 2006, by Lucas.
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01 Apr 15
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Additionally, every feasible solution for a linear program gives a bound on the optimal value of the objective function of its dual.
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31 Oct 14
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The linear-programming problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, but a larger theoretical and practical breakthrough in the field came in 1984 when Narendra Karmarkar introduced a new interior-point method for solving linear-programming problems.
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10 Sep 14
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26 May 14
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The problem of solving a system of linear inequalities dates back at least as far as Fourier, after whom the method of Fourier–Motzkin elimination is named. The linear programming method was first developed by Leonid Kantorovich in 1939.[1] Leonid Kantorovich developed the earliest linear programming problems in 1939 for use during World War II to plan expenditures and returns in order to reduce costs to the army and increase losses to the enemy. The method was kept secret until 1947 when George B. Dantzig published the simplex method and John von Neumann developed the theory of duality as a linear optimization solution, and applied it in the field of game theory. Postwar, many industries found its use in their daily planning.
The linear-programming problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, but a larger theoretical and practical breakthrough in the field came in 1984 when Narendra Karmarkar introduced a new interior-point method for solving linear-programming problems.
Dantzig's original example was to find the best assignment of 70 people to 70 jobs. The computing power required to test all the permutations to select the best assignment is vast; the number of possible configurations exceeds the number of particles in the observable universe. However, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the sim
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08 Feb 14
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The primal problem deals with physical quantities. With all inputs available in limited quantities, and assuming the unit prices of all outputs is known, what quantities of outputs to produce so as to maximize total revenue? The dual problem deals with economic values. With floor guarantees on all output unit prices, and assuming the available quantity of all inputs is known, what input unit pricing scheme to set so as to minimize total expenditure?
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The primal problem deals with physical quantities. With all inputs available in limited quantities, and assuming the unit prices of all outputs is known, what quantities of outputs to produce so as to maximize total revenue? The dual problem deals with economic values. With floor guarantees on all output unit prices, and assuming the available quantity of all inputs is known, what input unit pricing scheme to set so as to minimize total expenditure?
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To each variable in the primal space corresponds an inequality to satisfy in the dual space, both indexed by output type. To each inequality to satisfy in the primal space corresponds a variable in the dual space, both indexed by input type.
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In the primal space, this matrix expresses the consumption of physical quantities of inputs necessary to produce set quantities of outputs. In the dual space, it expresses the creation of the economic values associated with the outputs from set input unit prices.
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06 Jan 14
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two vectors are comparable when they have the same dimensions. If every entry in the first is less-than or equal-to the corresponding entry in the second then we can say the first vector is less-than or equal-to the second vector
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01 Nov 13
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03 Apr 13
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a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships.
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26 Mar 13
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07 Mar 13
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represented a
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the problem i
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08 Jan 13
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Its feasible region is a convex polyhedron
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The inequalities Ax ≤ b are the constraints which specify a convex polytope
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28 Aug 12
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25 Aug 12
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01 Mar 12
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09 Jan 12
carlos puentesLinear programming (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is a specific case of mathematical programming (mathematical optimization).
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19 Oct 11
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25 Feb 11
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17 Dec 10
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linear relationships.
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28 Nov 10
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One is the fact that (for the symmetric dual) the dual of a dual linear program is the original primal linear program
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06 Apr 10
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18 Dec 09
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03 Jun 09
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linear programming (LP) is a technique for optimization of a linear objective function, subject to linear equality and linear inequality constraints. Informally, linear programming determines the way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model and given some list of requirements represented as linear equations
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30 Mar 09
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01 Aug 08
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27 Mar 07
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08 Dec 06
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27 Dec 04
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