An Augmented Cubic Line Search Algorithm For Solving High-Dimensional Nonlinear Optimization Problems

Abstract

This paper presents a performance study of a one-dimensional search algorithm for solving general highdimensional nonlinear optimization problems. The proposed approach is a hybrid between the conventional cubic line search algorithm and a variant of Armijo’s line search algorithm. The resulting algorithm, called Augmented Cubic line search, was tested on some standard optimization problems, with a view to observing how optimization techniques for nonlinear optimization problems respond with increasing dimension. To this end, we report the successful performance of the algorithm on objective functions with 5, 000 and 10, 000 independent variables.