A filled function method for nonlinear systems of equalities and inequalities (Q712468)

The authors consider the following system of nonlinear equalities and inequalities defined by \(c_i= 0\), \(i\in E\) and \(c_j\leq 0\), \(j\in I\). The original problem is reformulated into an equivalent constrained global optimization problem of the following form \[ f(x)= \min_{x\in\mathbb{R}^n}\;{1\over 2}\,\Biggl\{\sum_{i\in E} c_i^2\Biggr\}\quad\text{s.t.}\quad c_j(x)\leq 0,\;j\in I. \] The authors present an algorithm based on the proposed filled function. Numerical experiments are also presented.