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Zbl 0581.65045
Vardi, Avi
A trust region algorithm for equality constrained minimization: Convergence properties and implementation. (English)
[J] SIAM J. Numer. Anal. 22, 575-591 (1985). ISSN 0036-1429; ISSN 1095-7170/e

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.
[S.Zabek]

MSC 2000:: *65K05 Mathematical programming (numerical methods)
90C30 Nonlinear programming

Keywords: numerical examples; nonlinear function; nonlinear constraints; trust region algorithms; superlinear convergence; numerical stability; test problems

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