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Parallel InteriorPoint Solver for Structured Quadratic Programs: Application to Financial Planning Problems
, 2003
"... Many practical largescale optimization problems are not only sparse, but also display some form of blockstructure such as primal or dual block angular structure. Often these structures are nested: each block of the coarse top level structure is blockstructured itself. Problems with these charact ..."
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Cited by 48 (19 self)
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Many practical largescale optimization problems are not only sparse, but also display some form of blockstructure such as primal or dual block angular structure. Often these structures are nested: each block of the coarse top level structure is blockstructured itself. Problems with these characteristics appear frequently in stochastic programming but also in other areas such as telecommunication network modelling. We present a linear algebra library tailored for problems with such structure that is used inside an interior point solver for convex quadratic programming problems. Due to its objectoriented design it can be used to exploit virtually any nested block structure arising in practical problems, eliminating the need for highly specialised linear algebra modules needing to be written for every type of problem separately. Through a careful implementation we achieve almost automatic parallelisation of the linear algebra. The efficiency of the approach is illustrated on several problems arising in the financial planning, namely in the asset and liability management. The problems are modelled as
Building and solving largescale stochastic programs on an affordable distributed computing system
 Annals of Operations Research
, 2000
"... ..."
A structureconveying modelling language for mathematical and stochastic programming
 Mathematical Programming Computation
, 2009
"... We present a structureconveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with objectoriented features that allows the user to construct models from submodels, and is implemented as a combination of preand postprocessing phases for AMPL. Unlike ..."
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Cited by 9 (2 self)
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We present a structureconveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with objectoriented features that allows the user to construct models from submodels, and is implemented as a combination of preand postprocessing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the problem, and thus it enables the passing of this structure on to the solver. Interior point solvers that exploit block linear algebra and decompositionbased solvers can therefore directly take advantage of the problem’s structure. The language contains features to conveniently model stochastic programming problems, although it is designed with a much broader application spectrum. 1
Customized Block Structures In Algebraic Modeling Languages: The Stochastic Programming Case
, 1998
"... Extracting complex block structures from an anonymous mathematical program is a difficult task. It is however a mandatory step to exploit them with adequate algorithmic techniques. Moreover, most economic models are usually built with an Algebraic Modeling Language (AML) which loose any structure. ..."
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Cited by 5 (4 self)
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Extracting complex block structures from an anonymous mathematical program is a difficult task. It is however a mandatory step to exploit them with adequate algorithmic techniques. Moreover, most economic models are usually built with an Algebraic Modeling Language (AML) which loose any structure. The recently developed concept SET (Structure Exploiting Tool) responds to these needs. This approach relates directly to the "semantic" of the original model that was used to generate the corresponding anonymous mathematical program. Examples from stochastic programming are presented.
A Planning Model with one Million Scenarios Solved on an A ordable Parallel Machine
, 1998
"... Stochastic programs inevitably get huge if they are to model real life problems accurately. Nowadays only massive parallel machines can solve them but at a cost few decision makers can afford. We report here on a deterministic equivalent linear programming model of 1,111,112 constraints and 2,555,55 ..."
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Cited by 4 (3 self)
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Stochastic programs inevitably get huge if they are to model real life problems accurately. Nowadays only massive parallel machines can solve them but at a cost few decision makers can afford. We report here on a deterministic equivalent linear programming model of 1,111,112 constraints and 2,555,556 variables generated by GAMS. It is solved by an interior point based decomposition method in less than 3 hours on a cluster of 10 Linux PC's.
SETSTOCH: A Tool for Multistage Stochastic Programming with Recourse
, 1998
"... SETSTOCH is a tool for linking Algebraic Modeling Languages (AMLs) with Specialized Stochastic Programming Solvers (SSPSs). Its main role is to retrieve from the AML a dynamically ordered core model (baseline scenario) that is then sent automatically to the SSPS. The user is then able to take full a ..."
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Cited by 1 (1 self)
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SETSTOCH is a tool for linking Algebraic Modeling Languages (AMLs) with Specialized Stochastic Programming Solvers (SSPSs). Its main role is to retrieve from the AML a dynamically ordered core model (baseline scenario) that is then sent automatically to the SSPS. The user is then able to take full advantage of specific SSPS features. The current implementation of SETSTOCH enables to access the SP/OSL subroutines via the GAMS modeling language. An example of energy planning is presented.
Approved by
, 2004
"... Interim Reports on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. –ii– ..."
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Interim Reports on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. –ii–
To appear in Mathematical Programming. 1 Parallel InteriorPoint Solver for Structured Linear Programs ∗
, 2000
"... Parallel InteriorPoint Solver for Structured Linear Programs Issues of implementation of an objectoriented library for parallel interiorpoint methods are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedd ..."
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Parallel InteriorPoint Solver for Structured Linear Programs Issues of implementation of an objectoriented library for parallel interiorpoint methods are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated reallife optimization problems can be modelled. The efficiency of the solver is illustrated on several problems arising in the optimization of networks. The sequential implementation outperforms the stateoftheart commercial optimization software. The parallel implementation achieves speedups of about 3.13.9 on 4processors parallel systems and speedups of about 1012 on 16processors parallel systems. Parallel InteriorPoint Solver for Structured Linear Programs 1 1