Geodesic
Generalized Newton method for linear optimization problems with inequality constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 98-108
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A dual problem of linear programming (LP) 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 on the set of solutions of the dual LP problem in dual and auxiliary variables is easily found by means of a single solution of an unconstrained maximization problem. The unconstrained maximization is carried out by the generalized Newton method, which is globally convergent in a finite number of steps. The results of numerical experiments are presented for randomly generated large-scale LP problems.
Keywords: linear programming problem, piecewise quadratic function, unconstrained maximization, generalized Newton method. 
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A. I. Golikov; Yu. G. Evtushenko. Generalized Newton method for linear optimization problems with inequality constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 98-108. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a9/

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