“…The filled function algorithm is an efficient deterministic global optimization algorithm, and it has been used to solve plenty of optimization problems, such as unconstrained global optimization problems [9,10], constrained global optimization problems [25], nonlinear equations [13,14,24], constrained nonlinear equations [1], nonlinear complementarity problems [27] and so on. The main idea of filled function method is to construct an auxiliary function called filled function via the current local minimizer of the original optimization problem, with the property that the current local minimizer is a local maximizer of the constructed filled function and a better initial point of the primal optimization problem can be obtained by searching the constructed filled function locally.…”