A. Forsgren and W. Murray, Newton methods for large-scale linear inequality-constrained minimization, SIAM J. Optim., 7 (1997), pp. 162--176. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Newton's Method For Large Bound-Constrained Optimization.. - Lin, Moré (1999) (16 citations) (Correct)
....problems has been established, in almost all cases, under the assumption of strict complementarity. Moreover, the algorithms that have been analyzed usually require the exact solution of systems of linear equations. See, for example, 2, 22, 33, 18] for algorithms that use # active constraints, [23, 20] for active set methods, 13, 25, 12, 21] for trust region methods, and [9, 16, 11, 10] for interior point methods. In recent work Heinkenschloss, Ulbrich, and Ulbrich [24] analyzed an interior point method without assuming strict complementarity, but they proved only local convergence. Lescrenier ....
....algorithms assert that every limit point of the algorithm is stationary, but they do not yield any information on the projected gradient; in sections 3 and 5 we show that (2.9) in Theorem 2.1 plays an important role in the convergence analysis. For a sampling of recent convergence results, see [12, 18, 9, 16, 20, 33]. 3. Exposing constraints. Identification properties are an important component of the convergence analysis of an algorithm for linearly constrained problems. We show that if x # is a stationary point and# is the polyhedral set (1.3) then the iterates x k generated by the trust region ....
[Article contains additional citation context not shown here]
A. Forsgren and W. Murray, Newton methods for large-scale linear inequality-constrained minimization, SIAM J. Optim., 7 (1997), pp. 162--176.
A Convergent Infeasible Interior-Point Trust-Region Method For.. - Tseng (1999) (1 citation) (Correct)
....and that (9) with # = 0 holds for all x # X 0 (see discussions after Prop. 3) The latter is weaker than the common regularity assumption of linear independence of #g i (x) i # I(x) The feasible active set Newton method of Forsgren and Murray for linear inequality constrained problems [14] also generates 2nd order stationary points, but assumes, instead of (9) with # = 0, that the problem does not have primal nondegenerate 2nd order stationary points. In the case of bound constraints (for which regularity holds everywhere) Coleman and Li [7] proposed a feasible a#ne scaling ....
....0 ) s 0 = 0, then the method maintains feasibility at all iterations and the above su#cient conditions can be refined to boundedness of the feasible set X 0 and 0 ## convex hull of #g i (x) i # I(x) for all x # X 0 . This contrasts with the su#cient conditions for the methods of [7, 14, 21]. If g is given by Example 1 and f is any thrice di#erentiable function defined on # 2 , then max #g(x 0 ) s 0 # # , max # 1 # 1 ( 1 2 is su#cient for x t generated by Algorithm 2 (with the same provision as above) to be defined, bounded, and all cluster points to ....
Forsgren, A. and Murray, W., Newton method for large-scale linear inequalityconstrained minimization, SIAM J. Optim., 7 (1997), 162-176.
Newton's Method for Large Bound-Constrained Optimization Problems - Lin, More (1998) (16 citations) (Correct)
....problems has been established, in almost all cases, under the assumption of strict complementarity. Moreover, the algorithms that have been analyzed usually require the exact solution of systems of linear equations. See, for example, 2, 22, 33, 18] for algorithms that use ffl active constraints, [23, 20] for active set methods, 13, 25, 12, 21] for trust region methods, and [9, 16, 11, 10] for interior point methods. In recent work Heinkenschloss, Ulbrich, and Ulbrich [24] analyzed an interior point method without assuming strict complementarity, but proved only local convergence. Lescrenier [25] ....
....algorithms assert that every limit point of the algorithm is stationary, but do not yield any information on the projected gradient; in Sections 3 and 5 we show that (2.9) in Theorem 2.1 plays an important role in the convergence analysis. For a sampling of recent convergence results, see [12, 18, 9, 16, 20, 33]. 3 Exposing Constraints Identification properties are an important component of the convergence analysis of an algorithm for linearly constrained problems. We show that if x is a stationary point and Omega is the polyhedral set (1.3) then the iterates fx k g generated by the trust region ....
[Article contains additional citation context not shown here]
A. Forsgren and W. Murray, Newton methods for large-scale linear inequalityconstrained minimization, SIAM J. Optim., 7 (1997), pp. 162--176.
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