Solving polynomial systems using a modified line search approach
Crina Groşan, Ajith Abraham, Václav Snåšel · 2012
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 sys-tem 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, chem-ical 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. 1. Introduction. Polynomial