Topographical global initialization for finding all solutions of nonlinear systems with constraints

• We apply the topographical global initialization to solve nonlinear systems.
• The nonlinear systems are subject to inequality constraints.
• The technique used is an ingenious approach based on concepts of graph theory.
• Solutions of global optimization problems are roots of the nonlinear systems.

We apply a recently revisited version of the topographical global initialization to solve nonlinear systems of equations with multiple roots subject to inequality constraints. This initialization technique is a simple and ingenious approach based on elementary concepts of graph theory. Here, the topographical initialization is used to generate good starting points to solve constrained global minimization problems, whose solutions are roots of associated nonlinear systems. To accomplish the task of local search, in the minimization step we use a well-established interior-point method. Our methodology was compared against other methods using benchmarks from the literature. Results indicated that the present approach is a powerful strategy for finding all roots of nonlinear systems.