Forsgren, Anders; Murray, Walter Newton methods for large-scale linear inequality-constrained minimization. (English) Zbl 0869.65039 SIAM J. Optim. 7, No. 1, 162-176 (1997). 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. Cited in 9 Documents MSC: 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming Keywords:linear inequality-constrained minimization; negative curvature; modified Newton method; symmetric indefinite factorization; linesearch method; large scale minimization; second-order necessary optimality conditions Citations:Zbl 0774.65034 Software:MINOS PDFBibTeX XMLCite \textit{A. Forsgren} and \textit{W. Murray}, SIAM J. Optim. 7, No. 1, 162--176 (1997; Zbl 0869.65039) Full Text: DOI