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A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables. (English) Zbl 0861.65053

The authors propose a new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. The method applies to a general (indefinite) quadratic function for which a local minimizer subject to bounds is required and is particularly suitable for the large scale problem. This new method exhibits strong convergence properties and global and second-order convergence and appears to have significant practical potential. Strictly feasible points are generated. The experimental results on moderately large and sparse problems based on both sparse Cholesky and preconditioned conjugate gradient linear solvers are presented.

MSC:

65K05 Numerical mathematical programming methods
90C20 Quadratic programming
90C06 Large-scale problems in mathematical programming

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