Total Hessian in Least Squares Optimization of Lens Design

2000 ◽  
Vol 29 (2) ◽  
pp. 95-104
Author(s):  
J. Basu ◽  
L. N. Hazra
Keyword(s):  
Least Squares ◽  
Lens Design ◽  
Least Squares Optimization

scholarly journals Method for the identification of explicit polynomial formulae for the friction in turbulent pipe flow

1999 ◽  
Vol 1 (2) ◽  
pp. 115-126 ◽  
Author(s):  
J. W. Davidson ◽  
D. Savic ◽  
G. A. Walters
Keyword(s):  
Least Squares ◽  
Symbolic Regression ◽  
Regression Method ◽  
Turbulent Pipe Flow ◽  
Model Complexity ◽  
Improve Performance ◽  
Rule Based ◽  
Least Squares Optimization ◽  
Starting Solutions ◽  
Crossover And Mutation

The paper describes a new regression method for creating polynomial models. The method combines numerical and symbolic regression. Genetic programming finds the form of polynomial expressions, and least squares optimization finds the values for the constants in the expressions. The incorporation of least squares optimization within symbolic regression is made possible by a rule-based component that algebraically transforms expressions to equivalent forms that are suitable for least squares optimization. The paper describes new operators of crossover and mutation that improve performance, and a new method for creating starting solutions that avoids the problem of under-determined functions. An example application demonstrates the trade-off between model complexity and accuracy of a set of approximator functions created for the Colebrook–White formula.

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