N. I. M. Gould, D. Orban, A. Sartenaer and P. L. Toint, Superlinear convergence of primal-dual interior point algorithms for nonlinear programming, SIAM J. Optim., 11 (2001), pp. 974-1002. Home/Search Document Details and Download
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Effects Of Finite-Precision Arithmetic On - Interior-Point Methods For (Correct)
....(3. 11) are imposed in most path following interior point methods for linear programming (see, for example, 26] For nonlinear convex programming, examples of methods that require these conditions can be found in Ralph and Wright [31, 21, 22] In nonlinear programming, we mention Gould et al. [14] (see Algorithm 4.1 and Figure 5.1) and Byrd, Liu, and Nocedal [4] In the latter paper, 3.11a) and (3.11b) are imposed explicitly, while (3.11c) can be guaranteed by choosing ffl = 1 Gamma fl) Even when the choice ffl = is made, as in the bulk of the discussion in [4] their other ....
N. I. M. Gould, D. Orban, A. Sartanaer, and P. Toint, Superlinear convergence of primal-dual interior-point algorithms for nonlinear programming, Technical Report TR/PA/00/20, CERFACS, April 2000.
Effects Of Finite-Precision Arithmetic On Interior-Point Methods.. - Wright (1998) (Correct)
....(3. 11) are imposed in most path following interior point methods for linear programming (see, for example, 27] For nonlinear convex programming, examples of methods that require these conditions can be found in Ralph and Wright [32, 23, 22] In nonlinear programming, we mention Gould et al. [14] (see Algorithm 4.1 and Figure 5.1) and Byrd, Liu, and Nocedal [4] In the latter paper, 3.11a) and (3.11b) are imposed explicitly, while (3.11c) can be guaranteed by choosing ffl = 1 Gamma fl) Even when the 8 STEPHEN J. WRIGHT choice ffl = is made, as in the bulk of the discussion in ....
N. I. M. Gould, D. Orban, A. Sartanaer, and P. Toint, Superlinear convergence of primal-dual interior-point algorithms for nonlinear programming, Technical Report TR/PA/00/20, CERFACS, April 2000.
Some Reflections on the Current State of Active-Set and.. - Gould (2003) Self-citation (Gould) (Correct)
....unwary. The asymptotic behaviour of interior point methods is relatively well understood even in the non convex case, at least under non degeneracy assumptions: the barrier parameter may be reduced at a superlinear rate so that the overall iteration converges superlinearly for primal dual methods [17] and 2 step superlinearly for primalonly methods [9] although the latter requires some care when reducing the barrier parameter. Some progress has been made in the degenerate case, but we do not currently have as complete an understanding as in the linear programming case where degeneracy does ....
N. I. M. Gould, D. Orban, A. Sartenaer, and Ph. L. Toint. Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. SIAM Journal on Optimization, 11(4):974-1002, 2001.
Componentwise Fast Convergence in the Solution of.. - Gould, Orban.. (2000) (1 citation) Self-citation (Gould Orban Sartenaer Toint) (Correct)
....recirculation regions and shock waves and thus to have control over the convergence of certain, prede ned, variables. Recently, it has been shown that the iterates generated by certain interior point methods for constrained optimization converge at a componentwise fast (almost quadratic) Q rate [6]. The methods we consider here are a variation, and generalization, on this theme. In what follows, we use the order notation for conciseness and clarity. If f k g and f k g are two sequences of positive numbers converging to zero, we say that k = o( k ) if lim k 1 k = k = 0, ....
....process which turns out to be superlinearly convergent. Note that in a primal dual interior point framework, the aforementioned problem does not arise, and the technique applied by Dussault is identical to Newton s method, which may result in a componentwise nearly quadratic Q rate of convergence [6]. Let f k g, f k g and f k g be strictly decreasing sequences of parameters whose limit are zero, and consider the iteration given in Algorithm 2.1 for solving (1.1) by way of (2.5) 6 N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint Algorithm 2.1: Parameterized root nding ....
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N. I. M. Gould, D. Orban, A. Sartenaer, and Ph. L. Toint. Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming. Technical Report TR/PA/00/20, CERFACS, Toulouse, France, 2000. 20 N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint
Interior-Point l_2-Penalty Methods for Nonlinear Programming.. - Chen, Goldfarb (2004) (Correct)
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N. I. M. Gould, D. Orban, A. Sartenaer and P. L. Toint, Superlinear convergence of primal-dual interior point algorithms for nonlinear programming, SIAM J. Optim., 11 (2001), pp. 974-1002.
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