A diagonal quadratic approximation method for large scale linear programs

John M. Mulvey; Andrzej Ruszczyński

doi:10.1016/0167-6377(92)90046-6

A diagonal quadratic approximation method for large scale linear programs

John M. Mulvey, Andrzej Ruszczyński

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58 Scopus citations

Abstract

An augmented Lagrangian method is proposed for handling the common rows in large scale linear programming problems with block-diagonal structure and linking constraints. Using a diagonal quadratic approximation of the augmented Lagrangian one obtains subproblems that can be readily solved in parallel by a nonlinear primal-dual barrier method for convex separable programs. The combined augmented Lagrangian/barrier method applies in a natural way to stochastic programming and multicommodity networks.

Original language	English (US)
Pages (from-to)	205-215
Number of pages	11
Journal	Operations Research Letters
Volume	12
Issue number	4
DOIs	https://doi.org/10.1016/0167-6377(92)90046-6
State	Published - Oct 1992

All Science Journal Classification (ASJC) codes

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

Keywords

decomposition
linear programming
stochastic programming

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10.1016/0167-6377(92)90046-6

Cite this

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title = "A diagonal quadratic approximation method for large scale linear programs",

abstract = "An augmented Lagrangian method is proposed for handling the common rows in large scale linear programming problems with block-diagonal structure and linking constraints. Using a diagonal quadratic approximation of the augmented Lagrangian one obtains subproblems that can be readily solved in parallel by a nonlinear primal-dual barrier method for convex separable programs. The combined augmented Lagrangian/barrier method applies in a natural way to stochastic programming and multicommodity networks.",

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author = "Mulvey, \{John M.\} and Andrzej Ruszczy{\'n}ski",

year = "1992",

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AU - Ruszczyński, Andrzej

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AB - An augmented Lagrangian method is proposed for handling the common rows in large scale linear programming problems with block-diagonal structure and linking constraints. Using a diagonal quadratic approximation of the augmented Lagrangian one obtains subproblems that can be readily solved in parallel by a nonlinear primal-dual barrier method for convex separable programs. The combined augmented Lagrangian/barrier method applies in a natural way to stochastic programming and multicommodity networks.

KW - decomposition

KW - linear programming

KW - stochastic programming

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VL - 12

SP - 205

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JO - Operations Research Letters

JF - Operations Research Letters

IS - 4

ER -

A diagonal quadratic approximation method for large scale linear programs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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