Solving nonlinear systems of functional equations with fuzzy adaptive simulated annealing

摘要

This paper proposes a method for finding solutions of arbitrarily nonlinear systems of functional equations through stochastic global optimization. The original problem (equation solving) is transformed into a global optimization one by synthesizing objective functions whose global minima, if they exist, are also solutions to the original system. The global minimization task is carried out by the stochastic method known as fuzzy adaptive simulated annealing, triggered from different starting points, aiming at finding as many solutions as possible. To demonstrate the efficiency of the proposed method, solutions for several examples of nonlinear systems are presented and compared with results obtained by other approaches. We consider systems composed of n equations on Euclidean spaces R~n (n variables: x_1, x_2, x_3, ..., x_n).