Parallel interior-point solver for structured quadratic programs: Application to financial planning problems

Many practical large-scale optimization problems are not only sparse, but also display some form of block-structure such as primal or dual block angular structure. Often these structures are nested: each block of the coarse top level structure is block-structured itself. Problems with these characte...

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Bibliographic Details
Published in:Annals of operations research Vol. 152; no. 1; pp. 319 - 339
Main Authors: Gondzio, Jacek, Grothey, Andreas
Format: Journal Article
Language:English
Published: New York Springer Nature B.V 01.07.2007
Subjects:
Algorithms
Exploitation
Linear algebra
Object oriented programming
Operations research
Optimization
Portfolio management
Random variables
Sparsity
Stochastic models
Studies
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary:Many practical large-scale optimization problems are not only sparse, but also display some form of block-structure such as primal or dual block angular structure. Often these structures are nested: each block of the coarse top level structure is block-structured 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 object-oriented 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 multistage decision processes and by nature lead to nested block-structured problems. By taking the variance of the random variables into account the problems become non-separable quadratic programs.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-006-0139-z