A new filled function method for nonlinear equations

A Novel Filled Function Method for Nonlinear Equations

“…Kanzow [3] incorporated two well-known global optimization algorithms, namely, a tunneling [7] and a filled function method [8], into a standard nonsmooth Newton-type method for solving a nonsmooth system of equations which is a reformulation of the mixed complementarity problem. Wu et al [9] and Lin et al [10,11] also gave some filled function methods to solve a nonlinear system with box constraints. Wang et al [12] gave a filled function method to solve an unconstrained nonlinear system.…”

“…The existence of local minimizers other than global ones makes global optimization a great challenge. As one of the main methods to solve general unconstrained or boxconstrained global optimization problems without special structural property, the filled function method has attracted extensive attention; see [8][9][10][11][12][13][14][15]. The main idea of the 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 minimizing the constructed filled function locally.…”

A filled function method for nonlinear systems of equalities and inequalities

“…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.…”