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Newton methods for large-scale linear inequality-constrained minimization. (English) Zbl 0869.65039

Summary: Newton methods of the linesearch type for large scale minimization subject to linear inequality constraints are discussed. The purpose of the paper is twofold: (i) to give an active-set-type method with the ability to delete multiple constraints simultaneously and (ii) to give a relatively short general convergence proof for such a method. It is also discussed how multiple constraints can be added simultaneously.
The approach is an extension of a previous work by the same authors for equality-constrained problems [SIAM J. Matrix Anal. Appl. 14, No. 2, 560-587 (1993; Zbl 0774.65034)]. It is shown how the search directions can be computed without the need to compute the reduced Hessian of the objective function. The convergence analysis states that every limit point of a sequence of iterates satisfies the second-order necessary optimality conditions.

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Citations:

Zbl 0774.65034

Software:

MINOS
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