Fourer, Robert
Overview
Works:  35 works in 112 publications in 2 languages and 552 library holdings 

Roles:  Author, Editor 
Classifications:  QA402.5, 519.702855133 
Publication Timeline
.
Most widely held works by
Robert Fourer
AMPL : a modeling language for mathematical programming by
Robert Fourer(
Book
)
64 editions published between 1993 and 2009 in English and held by 430 WorldCat member libraries worldwide
64 editions published between 1993 and 2009 in English and held by 430 WorldCat member libraries worldwide
Modeling languages and systems(
Book
)
5 editions published between 2001 and 2002 in English and held by 29 WorldCat member libraries worldwide
5 editions published between 2001 and 2002 in English and held by 29 WorldCat member libraries worldwide
Models of railroad passengercar requirements in the Northeast Corridor by
Robert Fourer(
Book
)
1 edition published in 1976 in English and held by 27 WorldCat member libraries worldwide
1 edition published in 1976 in English and held by 27 WorldCat member libraries worldwide
AMPL, a modeling language for mathematical programming : using the AMPL student edition under MSDOS by
Robert Fourer(
Book
)
6 editions published in 1993 in English and held by 10 WorldCat member libraries worldwide
6 editions published in 1993 in English and held by 10 WorldCat member libraries worldwide
AMPL : a modeling language for mathematical programming by
Robert Fourer(
Book
)
3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
A modern approach to computer systems for linear programming by
Robert Fourer(
Book
)
2 editions published in 1978 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1978 in English and held by 3 WorldCat member libraries worldwide
Finding embedded network rows in linear programs by
Robert E Bixby(
Book
)
in German and Undetermined and held by 3 WorldCat member libraries worldwide
in German and Undetermined and held by 3 WorldCat member libraries worldwide
AMPL PC student Version 2(
)
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Solving Staircase Linear Programs BY THE Simplex Method. 2. Pricing(
Book
)
1 edition published in 1979 in English and held by 2 WorldCat member libraries worldwide
This and a companion paper share one goal: to solve staircasestructured linear programs faster through adaptation of the algorithms of the modern simplex method. Their means are quite different however: whereas the preceding paper concentrated on 'inversion' algorithms that factorize the basis and solve linear systems, the present paper looks are 'pricing' algorithms that select a variable to enter the basis at each iteration. Pricing involves two sets of algorithms: computation algorithm that determine reduced costs of the nonbasic variables, and selection algorithms that choose among variables whose reduced costs are favorable. This paper develops staircase adaptations of both sorts of algorithms, and reports extensive (although preliminary) computational experience. Staircase computation algorithms appear to offer modest but consistent savings; staircase selection algorithms, properly chosen, may offer substantial savings in number of iterations, time per iteration, or sometimes both. (Author)
1 edition published in 1979 in English and held by 2 WorldCat member libraries worldwide
This and a companion paper share one goal: to solve staircasestructured linear programs faster through adaptation of the algorithms of the modern simplex method. Their means are quite different however: whereas the preceding paper concentrated on 'inversion' algorithms that factorize the basis and solve linear systems, the present paper looks are 'pricing' algorithms that select a variable to enter the basis at each iteration. Pricing involves two sets of algorithms: computation algorithm that determine reduced costs of the nonbasic variables, and selection algorithms that choose among variables whose reduced costs are favorable. This paper develops staircase adaptations of both sorts of algorithms, and reports extensive (although preliminary) computational experience. Staircase computation algorithms appear to offer modest but consistent savings; staircase selection algorithms, properly chosen, may offer substantial savings in number of iterations, time per iteration, or sometimes both. (Author)
Solving Staircase Linear Programs by the Simplex Method, 1: Inversion(
Book
)
1 edition published in 1979 in English and held by 2 WorldCat member libraries worldwide
Problems of economic planning, production scheduling, inventory, transportation, control and multistage structural design have been modeled as linear programs that have a 'staircase' structure: their activities fall into a sequence of disjoint stages or periods, while their constraints relate only successive periods. At one time it was hoped that staircase linear programs would be particularly easy to solve, owing to their special structure, but experience with the most common solution technique  the general simplex method  has shown otherwise. Over the years many alternatives to the simplex method have also been proposed, but as yet none of these has been proved superior in solving a wide variety of staircase problems. This and a companion paper consider how the modern simplex method  as implemented for large computers  may be adapted to solve staircase linear programs more efficiently. Each paper looks at a set of algorithms within the simplex method: this one deals with 'inversion' of the basis  more accurately, solution of linear systems by Gaussian elimination  and its successor considers the task of 'pricing'
1 edition published in 1979 in English and held by 2 WorldCat member libraries worldwide
Problems of economic planning, production scheduling, inventory, transportation, control and multistage structural design have been modeled as linear programs that have a 'staircase' structure: their activities fall into a sequence of disjoint stages or periods, while their constraints relate only successive periods. At one time it was hoped that staircase linear programs would be particularly easy to solve, owing to their special structure, but experience with the most common solution technique  the general simplex method  has shown otherwise. Over the years many alternatives to the simplex method have also been proposed, but as yet none of these has been proved superior in solving a wide variety of staircase problems. This and a companion paper consider how the modern simplex method  as implemented for large computers  may be adapted to solve staircase linear programs more efficiently. Each paper looks at a set of algorithms within the simplex method: this one deals with 'inversion' of the basis  more accurately, solution of linear systems by Gaussian elimination  and its successor considers the task of 'pricing'
Finding embedded network rows in linear programs I : extraction heuristics by
Robert E Bixby(
Book
)
2 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide
An embedded network within a linear program is, roughly speaking, a subset of constraints that represent conservation of flow. In this paper, we examine three broad classes of heuristic techniquesrowscanning deletion, column scanning deletion, and rowscanning additionfor the extraction of large embedded networks. We describe a variety of implementations, and compare their performance on varied test problems. The success of our tests depends, in part, on several preprocessing steps that scale the constraint matrix and that set aside certain rows and columns. Efficiency of the subsequent network extraction is dependent on the implementation, in predictable ways. Effectiveness is harder to explain; the more sophisticated and expensive implementations seem to be more reliable, but much simpler implementations sometimes find equally large networks. The largest networks are obtained by applying a final augmentation phase, which is studied in the second part of this paper
2 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide
An embedded network within a linear program is, roughly speaking, a subset of constraints that represent conservation of flow. In this paper, we examine three broad classes of heuristic techniquesrowscanning deletion, column scanning deletion, and rowscanning additionfor the extraction of large embedded networks. We describe a variety of implementations, and compare their performance on varied test problems. The success of our tests depends, in part, on several preprocessing steps that scale the constraint matrix and that set aside certain rows and columns. Efficiency of the subsequent network extraction is dependent on the implementation, in predictable ways. Effectiveness is harder to explain; the more sophisticated and expensive implementations seem to be more reliable, but much simpler implementations sometimes find equally large networks. The largest networks are obtained by applying a final augmentation phase, which is studied in the second part of this paper
Sparse Gaussian Elimination of Staircase Linear Systems(
Book
)
1 edition published in 1979 in English and held by 2 WorldCat member libraries worldwide
A square system of linear equations is said to be sparse if it can be solved most efficiently through a knowledge of its arrangement of zero and nonzero coefficients. Sparse systems are commonly solved by the techniques of sparse Gaussian elimination. An important class of sparse systems are those that have a 'staircase' structure: their variables fall into a natural sequence of disjoint groups, and each equation relates only variables within the group or within two adjacent groups. This paper proposes special methods of sparse Gaussian elimination for staircasestructured systems. These methods are particularly applicable to linear programming problems whose constraints have a staircase structure; they may also find application in solving staircase linear systems that arise in nonlinear optimization and optimal control. The initial sections of this paper present a selfcontained review of sparse elimination, and derive pertinent properties of staircase systems. Subsequent sections pursue two approaches to staircase elimination, and report initial computational experience in detail. (Author)
1 edition published in 1979 in English and held by 2 WorldCat member libraries worldwide
A square system of linear equations is said to be sparse if it can be solved most efficiently through a knowledge of its arrangement of zero and nonzero coefficients. Sparse systems are commonly solved by the techniques of sparse Gaussian elimination. An important class of sparse systems are those that have a 'staircase' structure: their variables fall into a natural sequence of disjoint groups, and each equation relates only variables within the group or within two adjacent groups. This paper proposes special methods of sparse Gaussian elimination for staircasestructured systems. These methods are particularly applicable to linear programming problems whose constraints have a staircase structure; they may also find application in solving staircase linear systems that arise in nonlinear optimization and optimal control. The initial sections of this paper present a selfcontained review of sparse elimination, and derive pertinent properties of staircase systems. Subsequent sections pursue two approaches to staircase elimination, and report initial computational experience in detail. (Author)
AMPL by
Robert Fourer(
Book
)
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
AMPL student edition(
)
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
AMPL by
Robert Fourer(
Book
)
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
An optimizationbased decision support system for strategic planning in a process industry : the case of an aluminium company
in India(
)
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide
AMPL by
Robert Fourer(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
XML modeling language for linear programming : specification and examples by
Robert Fourer(
Book
)
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
Database structures for mathematical programming models by
Robert Fourer(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Software survey : linear programming by
Robert Fourer(
)
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
more
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Audience Level
0 

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Kids  General  Special 
Related Identities
 Gay, David M.
 Kernighan, Brian W.
 Owen, Jonathan H. Editor
 Coullard, Collette Editor
 Transportation Systems Center
 United States Northeast Corridor Project Office
 United States Federal Railroad Administration
 National Bureau of Economic Research
 Bixby, Robert E. Author
 STANFORD UNIV CALIF SYSTEMS OPTIMIZATION LAB
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