An Alternative Scaling Factor In Broyden's Class Methods for Unconstrained Optimization

Abstract

Problem statement: In order to calculate step size, a suitable line search method can be employed. As the step size usually not exact, the error is unavoidable, thus radically affect quasi-Newton method by as little as 0.1 percent of the step size error. Approach: A suitable scaling factor has to be introduced to overcome this inferiority. Self-scaling Variable Metric algorithms (SSVM's) are commonly used method, where a parameter is introduced, altering Broyden's single parameter class of approximations to the inverse Hesssian to a double parameter class. This study proposes an alternative scaling factor for the algorithms. Results: The alternative scaling factor had been tried on several commonly test functions and the numerical results shows that the new scaled algorithm shows significant improvement over the standard Broyden's class methods. Conclusion: The new algorithm performance is comparable to the algorithm with initial scaling on inverse Hessian approximation by step size. An improvement over unscaled BFGS is achieved, as for most of the cases, the number of iterations are reduced.