A Novel Filled Function Algorithm for System of Nonlinear Equations

Nonlinear equations are challenging problems arising in numerous applications. A widely adopted strategy is to transform nonlinear systems into equivalent global optimization problems whose objective function achieves its global minimum at the solution of the original system. The filled function algorithm, as an effective global optimization method, has attracted attention by continuously escaping from local minimizers until the global one is reached. In this paper, a novel parameter-free filled function without logarithmic and exponential terms is constructed for solving nonlinear equations, which overcomes several limitations of conventional filled functions. More importantly, it has the same local minimizers as the objective function, all of which are better than the current one. Accordingly, in the proposed filled function algorithm, the objective function needs to be minimized only once, which breaks the conventional framework of alternately minimizing the filled function and the objective function, effectively reducing the number of local optimizations and accelerating global optimization. Finally, numerical experiments demonstrate that the proposed algorithm is feasible and effective.