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Parameter Optimization for Equilibrium Solutions of Mass Action Systems

Johansson, Edvard LU and Petersson, David LU (2016) In Master’s Theses in Mathematical Sciences FMA820 20161
Mathematics (Faculty of Engineering)
Abstract
In this thesis, functions describing relations between chemical concentrations at equilibrium are studied. The functions have some parameters that are desired to be determined. Based on the properties of the functions, an optimization method will be proposed. Because of these special properties, it is appropriate to consider the residuals in the max norm, since then it is possible to show that there are only global minima. The existence of only global minima was proven by developing a theorem about preservation of strict quasiconvexity under the max operator.

An algorithm is presented that finds a minimum in the max norm. The performance of this algorithm is compared to the performance of other algorithms. Primarily it is compared to... (More)
In this thesis, functions describing relations between chemical concentrations at equilibrium are studied. The functions have some parameters that are desired to be determined. Based on the properties of the functions, an optimization method will be proposed. Because of these special properties, it is appropriate to consider the residuals in the max norm, since then it is possible to show that there are only global minima. The existence of only global minima was proven by developing a theorem about preservation of strict quasiconvexity under the max operator.

An algorithm is presented that finds a minimum in the max norm. The performance of this algorithm is compared to the performance of other algorithms. Primarily it is compared to optimization in the least square sense, since the least square norm is assumed to be better suited for the noise that is likely to be added to the points when making measurements. It was found that the proposed max norm algorithm worked well for the functions, but when the number of parameters and the deviation of the data points increased, the results were not satisfactory. (Less)
Popular Abstract (Swedish)
Inom hjärnforskning önskar man ta reda på värdet för olika kemiska parametrar. Här beskrivs en metod som med ren matematik kan beräkna de optimala parametervärdena. Den bakomliggande kemin gav upphov till speciella matematiska egenskaper. Med hjälp av en egenutvecklad sats kunde det då visas att metoden alltid hittar den lösning som är bäst enligt den så kallade maxnormen.
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author
Johansson, Edvard LU and Petersson, David LU
supervisor
organization
course
FMA820 20161
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Parameter Optimization, Strict Quasiconvexity, Strict Quasilinearity Infinity Norm, Max Norm
publication/series
Master’s Theses in Mathematical Sciences
report number
LUTFMA-3300-2016
ISSN
1404-6342
other publication id
2016:E37
language
English
id
8892543
date added to LUP
2016-10-05 13:27:39
date last changed
2016-10-05 13:27:39
@misc{8892543,
  abstract     = {In this thesis, functions describing relations between chemical concentrations at equilibrium are studied. The functions have some parameters that are desired to be determined. Based on the properties of the functions, an optimization method will be proposed. Because of these special properties, it is appropriate to consider the residuals in the max norm, since then it is possible to show that there are only global minima. The existence of only global minima was proven by developing a theorem about preservation of strict quasiconvexity under the max operator. 

An algorithm is presented that finds a minimum in the max norm. The performance of this algorithm is compared to the performance of other algorithms. Primarily it is compared to optimization in the least square sense, since the least square norm is assumed to be better suited for the noise that is likely to be added to the points when making measurements. It was found that the proposed max norm algorithm worked well for the functions, but when the number of parameters and the deviation of the data points increased, the results were not satisfactory.},
  author       = {Johansson, Edvard and Petersson, David},
  issn         = {1404-6342},
  keyword      = {Parameter Optimization,Strict Quasiconvexity,Strict Quasilinearity Infinity Norm,Max Norm},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master’s Theses in Mathematical Sciences},
  title        = {Parameter Optimization for Equilibrium Solutions of Mass Action Systems},
  year         = {2016},
}