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A trust region algorithm for equality constrained minimization: Convergence properties and implementation. (English) Zbl 0581.65045
The paper discusses iterative methods to minimize a smooth nonlinear function f(x), $f: {\bbfR}\sp n\to {\bbfR}$, subject to nonlinear constraints $h\sb j(x)=0$, $h\sb j: {\bbfR}\sp n\to {\bbfR}$, $j=1,2,...,m$, $m<n$. The author proposes to transfer the idea of trust region algorithms for unconstrained minimization onto such equality constrained minimization, developing a new trust region strategy. The algorithm is analyzed and its superlinear convergence (global as well as local one) is proved. The author describes also details of the implementation of the algorithm, guaranteeing its numerical stability. The corresponding computer program was tested for 12 test problems. The numerical results are presented and discussed.
Reviewer: S.Ząbek

65K05Mathematical programming (numerical methods)
90C30Nonlinear programming
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