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Mathematical Programming, 2015
This paper considers the problems of maximization and minimization of the spectral radius for nonnegative matrices with independent row uncertainties. The author proves necessary theoretical results on on-row corrections of nonnegative matrices. The spectral simplex methods for maximizing and minimizing the spectral radius are proposed.
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This paper considers the problems of maximization and minimization of the spectral radius for nonnegative matrices with independent row uncertainties. The author proves necessary theoretical results on on-row corrections of nonnegative matrices. The spectral simplex methods for maximizing and minimizing the spectral radius are proposed.
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Management Science, 1967
This paper presents a method, called the convex simplex method, for minimizing a convex objective function subject to linear inequality constraints. The method is a true generalization of Dantzig's linear simplex method both in spirit and in the fact that the same tableau and variable selection techniques are used. With a linear objective function the
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This paper presents a method, called the convex simplex method, for minimizing a convex objective function subject to linear inequality constraints. The method is a true generalization of Dantzig's linear simplex method both in spirit and in the fact that the same tableau and variable selection techniques are used. With a linear objective function the
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ACM SIGAPL APL Quote Quad, 1985
The following documented algorithm solves the standard linear programming problem of optimizing a linear form subject to linear inequality or equality constraints and nonnegativity conditions. The solution procedure incorporates the standard simplex method with no embellishments. There is only one loop corresponding to the basic simplex iteration.
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The following documented algorithm solves the standard linear programming problem of optimizing a linear form subject to linear inequality or equality constraints and nonnegativity conditions. The solution procedure incorporates the standard simplex method with no embellishments. There is only one loop corresponding to the basic simplex iteration.
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Inductive Proof of the Simplex Method
IBM Journal of Research and Development, 1960Instead of the customary proof of the existence of an optimal basis in the simplex method based on perturbation of the constant terms, this paper gives a new proof based on induction. From a pedagogical point of view it permits an earlier and more elementary proof of the fundamental duality theorem via the simplex method.
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2000
Based on the example described in Section 1.1, the idea for solving general linear programs with the Simplex Method can be motivated as follows:
Horst W. Hamacher, Kathrin Klamroth
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Based on the example described in Section 1.1, the idea for solving general linear programs with the Simplex Method can be motivated as follows:
Horst W. Hamacher, Kathrin Klamroth
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2008
The idea of the simplex method is to proceed from one basic feasible solution (that is, one extreme point) of the constraint set of a problem in standard form to another, in such a way as to continually decrease the value of the objective function until a minimum is reached. The results of Chap.
David G. Luenberger, Yinyu Ye
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The idea of the simplex method is to proceed from one basic feasible solution (that is, one extreme point) of the constraint set of a problem in standard form to another, in such a way as to continually decrease the value of the objective function until a minimum is reached. The results of Chap.
David G. Luenberger, Yinyu Ye
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2001
In this chapter we present the simplex method as it applies to linear programming problems in standard form.
Mik Wisniewski, Jonathan H. Klein
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In this chapter we present the simplex method as it applies to linear programming problems in standard form.
Mik Wisniewski, Jonathan H. Klein
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2003
In 1947, George Dantzig [51] developed an efficient method, the simplex algorithm, for solving linear programming problems. Since the development of the simplex method, LP has been used to solve optimization problems any where where there appears a necessity of optimizing some absolute criteria. It might be, for example, cost of trucking, profit gained
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In 1947, George Dantzig [51] developed an efficient method, the simplex algorithm, for solving linear programming problems. Since the development of the simplex method, LP has been used to solve optimization problems any where where there appears a necessity of optimizing some absolute criteria. It might be, for example, cost of trucking, profit gained
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1971
The simplex method was invented by Dantzig and was first published in 1951. It can be used to solve any linear programming problem, once it has been put into canonical form. Its name derives from the geometrical ‘simplex’, as one of the first problems to be solved by the method contained the constraint \(\sum\limits_{i = 1}^{n + 1} {{x_i} = 1} \) .
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The simplex method was invented by Dantzig and was first published in 1951. It can be used to solve any linear programming problem, once it has been put into canonical form. Its name derives from the geometrical ‘simplex’, as one of the first problems to be solved by the method contained the constraint \(\sum\limits_{i = 1}^{n + 1} {{x_i} = 1} \) .
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Advances in the Parallelization of the Simplex Method
2015The simplex method has been successfully used in solving linear programming problems for many years. Parallel approaches for the simplex method have been extensively studied in the literature due to the intensive computations required, especially for the solution of large linear problems (LPs).
Basilis Mamalis, Grammati E. Pantziou
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