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A filled function method for nonlinear systems of equalities and inequalities. (English) Zbl 1259.65095
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.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C26 Nonconvex programming, global optimization
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