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The generalized simplex method
Operations Research Letters, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Domingos M. Cardoso +1 more
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Central European Journal of Operations Research, 2014
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Csaba I. Fábián +2 more
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Csaba I. Fábián +2 more
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Parallelizing the Dual Simplex Method
INFORMS Journal on Computing, 2000We study the parallelization of the steepest-edge version of the dual simplex algorithm. Three different parallel implementations are examined, each of which is derived from the CPLEX dual simplex implementation. One alternative uses PVM, one general-purpose System V shared-memory constructs, and one the PowerC extension of C on a Silicon Graphics ...
Robert E. Bixby, Alexander Martin 0001
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A Simplex Method for Function Minimization
The Computer Journal, 1965A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is
John A. Nelder, R. Mead
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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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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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Mathematical Programming, 1976
Simple combinatorial modifications are given which ensure finiteness in the primal simplex method for the transshipment problem and the upper-bounded primal simplex method for the minimum cost flow problem. The modifications involve keeping "strongly feasible" bases.
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Simple combinatorial modifications are given which ensure finiteness in the primal simplex method for the transshipment problem and the upper-bounded primal simplex method for the minimum cost flow problem. The modifications involve keeping "strongly feasible" bases.
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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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