Open Access
2014 Numerical Reduced Variable Optimization Methods via Implicit Functional Dependence with Applications
Christopher Gunaseelan Jesudason
Abstr. Appl. Anal. 2014(SI37): 1-13 (2014). DOI: 10.1155/2014/108184


A systematic theoretical basis is developed that optimizes an arbitrary number of variables for (i) modeling data and (ii) the determination of stationary points of a function of several variables by the optimization of an auxiliary function of a single variable deemed the most significant on physical, experimental or mathematical grounds from which all the other optimized variables may be derived. Algorithms that focus on a reduced variable set avoid problems associated with multiple minima and maxima that arise because of the large numbers of parameters. For (i), both approximate and exact methods are presented, where the single controlling variable k of all the other variables Pk passes through the local stationary point of the least squares metric. For (ii), an exact theory is developed whereby the solution of the optimized function of an independent variation of all parameters coincides with that due to single parameter optimization of an auxiliary function. The implicit function theorem has to be further qualified to arrive at this result. A nontrivial real world application of the above implicit methodology to rate constant and final concentration parameter determination is made to illustrate its utility. This work is more general than the reduction schemes for conditional linear parameters since it covers the nonconditional case as well and has potentially wide applicability.


Download Citation

Christopher Gunaseelan Jesudason. "Numerical Reduced Variable Optimization Methods via Implicit Functional Dependence with Applications." Abstr. Appl. Anal. 2014 (SI37) 1 - 13, 2014.


Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07021749
MathSciNet: MR3256236
Digital Object Identifier: 10.1155/2014/108184

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI37 • 2014
Back to Top