Solving polynomial systems using a modified line search approach

Abstract

This paper proposes a modified line search technique for solving systems of complex nonlinear equations. Line search is a widely used iterative global search method. Since optimization strategies have been (and continue to be) successfully used for solving systems of nonlinear equations, the system is reduced to a one-dimensional equation system for optimization purpose. The proposed line search procedure incorporates a re-start technique, which makes use of derivatives to reduce the search space and to re-generate thereafter the starting points in between the new ranges. Several well known applications such as interval arithmetic benchmark, kinematics, neuropsychology, combustion, chemical equilibrium and economics application are considered for testing the performances of the proposed approach. To validate the strength of the proposed approach, systems having between 5 and 20 equations are considered. Results are compared with an evolutionary algorithm approach, which transforms the problem into a multi-objective optimization problem. Empirical results reveal that the proposed approach is able to deal with high dimensional equations systems very effectively.