An improved Levenberg–Marquardt method for nonsmooth equations with application to multi-stream heat exchangers

Abstract

Systems of nonsmooth equations are very useful in the study of nonlinear complementarity problems, variational inequality problems, bilevel programming problems, and arise in the mathematical modeling of many problems in chemical processing, mechanics and engineering. In this paper, we introduce a hybrid method for solving systems of nonsmooth equations, which combines the idea of Levenberg–Marquardt–type methods with bundle techniques, while avoiding the hypothesis of differentiability of the least squares merit function. Some numerical results comparing the proposed method with LP-Newton method indicate that the improved Levenberg–Marquardt algorithm works quite well in practice. As an application of the proposed algorithm, we consider the multi-stream heat exchanger network problem, where a heat exchange network must be designed to meet a specified exit temperature for a given set of streams.