A new method to optimize parameters in solutions of eclipsing binary light curves

Abstract

Optimization procedures currently in use in the solution of eclipsing binary light curves require calculation of partial derivatives of received light with respect to the system parameters. Complications often arise in achieving convergence with differential correction techniques. These complications may result from an initial parameter set that is too remote from the corrected solution, inaccurate calculated derivatives, parameter correlations, or an ill-conditioned set of normal equations. An optimization procedure, the simplex algorithm, is presented which cannot diverge, requires no calculated partial derivatives, is capable of automatic iteration, is operationally stable, and is computationally efficient. An application to MR Cygni data, using individual observations rather than normal points, illustrates the operation of the method.