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Global convergence of a class of trust region algorithms for optimization with simple bounds. (English) Zbl 0643.65031
This paper extends the known global convergence properties of trust region algorithms for un-constrained optimization to the case where bounds on the variables are presented in the form f(x)\(=^{!}Min\), \(\ell_ i\leq x_ i\leq u_ i\), \((i=1,...,n)\). These extensions are obtained by generalizing the classical notion of Cauchy point and by considering generaion see Zbl 0641.00024.]
For the problem: \(\epsilon y''+p(x)y'=f(x)\), \(-\alpha y(0)+y'(0)=\alpha_ 0\), \(y(1)=\alpha_ 1\), p(x)\(\geq \bar p>0\), the cubic spline collocation method is derived. Uniform convergence of first order on locally bounded mesh is achieved. The method has second order convergence for fixed \(\epsilon\).

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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