Generalized Newton method for linear optimization problems with inequality constraints |
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Authors: | A I Golikov Yu G Evtushenko |
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Institution: | 1.Dorodnitsyn Computing Centre,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | A dual problem of linear programming is reduced to the unconstrained maximization of a concave piecewise quadratic function for sufficiently large values of a certain parameter. An estimate is given for the threshold value of the parameter starting from which the projection of a given point to the set of solutions of the dual linear programming problem in dual and auxiliary variables is easily found by means of a single solution of the unconstrained maximization problem. The unconstrained maximization is carried out by the generalized Newton method, which is globally convergent in an a finite number of steps. The results of numerical experiments are presented for randomly generated large-scale linear programming problems. |
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