Introducing Powell's Direction Set Method to a Fully Automated Analysis of Eclipsing Binary Stars

Abstract

With recent observational advancements, substantial amounts of photometric and spectroscopic eclipsing binary data have been acquired. As part of an ongoing effort to assemble a reliable pipeline for fully automatic data analysis, we put Powell's direction set method to the test. The method does not depend on numerical derivatives, only on function evaluations, and as such it cannot diverge. Compared to differential corrections (DC) and Nelder & Mead's downhill simplex (NMS) method, Powell's method proves to be more efficient in terms of solution determination and the required number of iterations. However, its application is still not optimal in terms of time cost. Causes for this deficiency are identified and two steps toward the solution are proposed: non-ortogonality of the parameter set should be removed and better initial directions should be determined before the minimization is initiated. Once these setbacks are worked out, Powell's method will probably replace DC and NMS as the default minimizing algorithm in PHOEBE modeling package.