TY - GEN
T1 - Solving Multiscale Linear Programs Using the Simplex Method in Quadruple Precision
AU - Ma, Ding
AU - Saunders, Michael A.
PY - 2015
Y1 - 2015
N2 - Systems biologists are developing increasingly large models of metabolism and integrated models of metabolism and macromolecular expression. These Metabolic Expression (ME) models lead to sequences of multiscale linear programs for which small solution values of order 10−6 to 10−10 are meaningful. Standard LP solvers do not give sufficiently accurate solutions, and exact simplex solvers are extremely slow. We investigate whether double-precision and quadruple-precision simplex solvers can together achieve reliability at acceptable cost.A double-precision LP solver often provides a reasonably good starting point for a Quad simplex solver. On a range of multiscale examples we find that 34-digit Quad floating-point achieves exceptionally small primal and dual infeasibilities (of order 10−30) when no more than 10−15 is requested. On a significant ME model we also observe robustness in almost all (even small) solution values following relative perturbations of order 10−6 to non-integer data values.Double and Quad Fortran 77 implementations of the linear and nonlinear optimization solver MINOS are available upon request.
AB - Systems biologists are developing increasingly large models of metabolism and integrated models of metabolism and macromolecular expression. These Metabolic Expression (ME) models lead to sequences of multiscale linear programs for which small solution values of order 10−6 to 10−10 are meaningful. Standard LP solvers do not give sufficiently accurate solutions, and exact simplex solvers are extremely slow. We investigate whether double-precision and quadruple-precision simplex solvers can together achieve reliability at acceptable cost.A double-precision LP solver often provides a reasonably good starting point for a Quad simplex solver. On a range of multiscale examples we find that 34-digit Quad floating-point achieves exceptionally small primal and dual infeasibilities (of order 10−30) when no more than 10−15 is requested. On a significant ME model we also observe robustness in almost all (even small) solution values following relative perturbations of order 10−6 to non-integer data values.Double and Quad Fortran 77 implementations of the linear and nonlinear optimization solver MINOS are available upon request.
KW - Flux balance analysis
KW - Metabolic expression model
KW - Multiscale linear program
KW - Simplex method
KW - Quadruple precision
KW - Gfortran libquadmath
KW - MINOS
UR - http://www.scopus.com/inward/record.url?scp=84947073615&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84947073615&origin=recordpage
U2 - 10.1007/978-3-319-17689-5_9
DO - 10.1007/978-3-319-17689-5_9
M3 - 32_Refereed conference paper (with ISBN/ISSN)
SN - 9783319176888
T3 - Springer Proceedings in Mathematics & Statistics
SP - 223
EP - 235
BT - Numerical Analysis and Optimization
A2 - Al-Baali, Mehiddin
A2 - Grandinetti, Lucio
A2 - Purnama, Anton
PB - Springer International Publishing Switzerland
T2 - 3rd International Conference on Numerical Analysis and Optimization (NAO-III 2014)
Y2 - 5 January 2014 through 9 January 2014
ER -