Parametric linear programming techniques for the indefnite quadratic programming problem

by: Luis N Vicente, Joaquim J Judice, Panos M Pardalos

IMA J Management Math, Vol. 4, No. 4. (1 January 1992), pp. 343-349.

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摘要

In this paper, we discuss a multiparametric technique for finding a global minimum for an indefinite quadratic programming problem based on the spectral decomposition of the matrix of the quadratic form. Special attention is given to the case where this matrix has only rank 1, where the multiparametric linear program turns out to be a single-parameter linear program. An extension of the traditional linear parametric procedure is introduced which in general solves this problem efficiently. However, an example is presented showing that this technique may take an exponential number of steps. 10.1093/imaman/4.4.343

@article{citeulike:2813766, abstract = {In this paper, we discuss a multiparametric technique for finding a global minimum for an indefinite quadratic programming problem based on the spectral decomposition of the matrix of the quadratic form. Special attention is given to the case where this matrix has only rank 1, where the multiparametric linear program turns out to be a single-parameter linear program. An extension of the traditional linear parametric procedure is introduced which in general solves this problem efficiently. However, an example is presented showing that this technique may take an exponential number of steps. 10.1093/imaman/4.4.343}, author = {Vicente, Luis N. and Judice, Joaquim J. and Pardalos, Panos M. }, citeulike-article-id = {2813766}, doi = {http://dx.doi.org/10.1093/imaman/4.4.343}, journal = {IMA J Management Math}, keywords = {linear, multiplicative, programming, quadratic}, month = {January}, number = {4}, pages = {343--349}, posted-at = {2008-05-19 18:55:58}, priority = {4}, title = {Parametric linear programming techniques for the indefnite quadratic programming problem}, url = {http://dx.doi.org/10.1093/imaman/4.4.343}, volume = {4}, year = {1992} }

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TY - JOUR ID - citeulike:2813766 L3 - citeulike-article-id:2813766 N2 - In this paper, we discuss a multiparametric technique for finding a global minimum for an indefinite quadratic programming problem based on the spectral decomposition of the matrix of the quadratic form. Special attention is given to the case where this matrix has only rank 1, where the multiparametric linear program turns out to be a single-parameter linear program. An extension of the traditional linear parametric procedure is introduced which in general solves this problem efficiently. However, an example is presented showing that this technique may take an exponential number of steps. 10.1093/imaman/4.4.343 IS - 4 JF - IMA J Management Math EP - 349 TI - Parametric linear programming techniques for the indefnite quadratic programming problem VL - 4 SP - 343 KW - linear KW - multiplicative KW - programming KW - quadratic AU - Vicente, Luis AU - Judice, Joaquim AU - Pardalos, Panos PY - 1992/01/01/ UR - http://dx.doi.org/10.1093/imaman/4.4.343 ER -

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