T. Schlik and A. Fogelson, "TNPACK-A truncated Newton minimization package for large-scale problems: I. Algorithm and usage," ACM Transactions on Mathematical Software, vol. 18, no. 1, pp. 46--70, March 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of simple polyhedra, as these have the advantage that every vertex is easily parameterized by the twelve coefficients of its three incident planes. For the minimization, we use TNPACK, a freely available package specially suited for large scale problems with possibly thousands of variables [11]. To minimize a function F (X)#X2 TNPACK implements the iterative truncated Newton method, based on minimizing a local quadratic approximation to F at every step. For efficiency, an approximated (truncated) solution of this local minimization is allowed, which is computed through a ....

T. Schlik and A. Fogelson. TNPACK-A truncated Newton minimization package for large-scale problems: I. Algorithm and usage. ACM Transactions on Mathematical Software, 18(1):46--70, March 1992.

....If 6krf then the TN method will converge quadratically, see [6,33, 34, p. 393) This fact explains the faster rate of convergence and the better quality of results obtained with the TN method. Similar conclusions and more detailed discussion of the TN method can be found at [25,29 32,47]. o Pages 2267, DTD= 4.3.1 4. Phenomenological (explicit) viscoplastic creep model 4.1. Analytical model description For the purpose of comparison, the outline of an explicit viscoplastic model is presented here. A detailed investigation about this model can be found in earlier investigation ....

T. Schlick, A. Fogelson, TNPACK: A truncated Newton minimization package forlarge-#IWB problems: I. algorithm and usage, ACM Trans. Math. Soft. 18 (1992) 46--70.

....is appropriate to use a Hessian free truncated Newton method. This class of algorithm dates back to Dembo, Eisenstat and Steihaug [3] and O Leary [11] It has proved quite useful [4, 8, 9, 14] and various source codes are available from netlib (BTN [10] in toms 711, TN [7] in opt tn, and TNPACK [13] in toms 702) In what follows we will develop a version of the algorithm gradually, considering implementation issues as we go. The intent is not to derive some universally applicable method, but to reveal how small details contribute to robust performance. The basic algorithm outline is that of ....

....[7, 8] replaces (6) with a test that stops the CG loop when the model function OE k (d) fails to decrease substantially. It is also common to end the inner CG loop after a maximum number of iterations, usually some fraction of the number of unknowns n. Examples range from minf50; n=2g [7] to n [13]. The choice of oe in (9) is quite important when calculating minima to high accuracy. A small value of oe reduces the error due to Taylor series truncation, but magnifies roundoff errors made in computing the gradient rf . The ideal oe balances these two errors, but it cannot be computed without ....

T. Schlick and A. Fogelson. TNPACK -- a truncated Newton minimization package for large-scale problems: I. algorithm and usage. ACM Trans. Math. Softw., 18:46--70, 1992.

....(0)j: 1:2) The development of a search procedure that satisfies these conditions is a crucial ingredient in a line search method for minimization. The search algorithm described in this paper has been used by several authors, for example, Liu and Nocedal [10] O Leary [12] Schlick and Fogelson [14, 15], and Gilbert and Nocedal [7] This paper describes this search procedure and the associated convergence theory. In a line search method we are given a continuously differentiable function f : IR n IR and a descent direction p for f at a given point x 2 IR n . Thus, if OE(ff) j f(x ffp) ....

T. Schlick and A. Fogelson, TNPACK -- A truncated Newton minimization package for large-scale problemns: I. Algorithms and usage, ACM Trans. Math. Software, 18 (1992), pp. 46--70.

....is not surprising that the standard truncated Newton method required more computing time than the limited memory variable metric method. We expect that a truncated Newton method with a suitable preconditioner will reduce the computing time required to solve cluster problems. Schlick and Fogelson [45, 46] developed such an algorithm for molecular dynamics simulation and structure refinement, with a preconditioner constructed from an approximate Hessian matrix. Similar ideas should apply to cluster problems. 5.4 Function Evaluations We have already noted that the number of flops required to ....

T. Schlick and A. Fogelson, TNPACK -- A truncated Newton minimization package for large-scale problems: I. Algorithms and usage, ACM Trans. Math. Software, 18 (1992), pp. 46--70.

....and we want to satisfy (1) at least approximately, for the pairs in the data base. To make best use of current optimization technology, it is desirable to have a smooth (i.e. twice continuously differentiable with respect to x) potential. This allows for robust local optimization (e.g. [3,20]) and can be combined with global search techniques such as simulated annealing (e.g. 13,26] genetic algorithms (e.g. 8,25] smoothing methods (e.g. 17,14] or branch and bound techniques (e.g. 16] to approach the global minimizer for sequences s with unknown native geometry. ....

T. Schlick and A. Fogelson, TNPACK -- A truncated Newton minimization package for large scale problems, ACM Trans. Math. Softw. 18 (1992), 46-70; 71-111.

....1 INTRODUCTION 2 Each barrier function will be minimized by a truncated Newton method. We approximate an inverse preconditioning matrix by a truncated Lanczos decomposition of (r 2 xx ) Gamma1 . In contrast to the truncated Newton method proposed in [Nash, 1984] or [Schlick and Fogelson, 1992] we compute Gamma r 2 xx (x; w; s) Delta Gamma1 Q V D Gamma1 V T Q T with n ; directly and use it as an approximation of the inverse Hessian. Here V D V T 2 R Theta is the spectral decomposition of the tridiagonal matrix T generated in the Lanczos algorithm and ....

Schlick, T. , Fogelson, A. : TNPACK - A Truncated Newton Minimization Package for Large-Scale Problems ; Transactions on Mathematical Software 18 (No. 1) : 46-70 (1992)

....limit the amount of work done at each iteration. A comparison of these methods developed by chemists with some of the recent methods for large scale optimization developed by the optimization community, in particular truncated Newton methods (Nash [217] Schlick Overton [276] Schlick Fogelson [274]) is given in a recent survey article by Schlick [273] For an adaptation of the truncated Newton optimization package TNPACK [274] to the molecular mechanics package CHARMM [33] see Derreumaux et al. 76] However, since the objective function has a huge number of local minima, a local ....

.... for large scale optimization developed by the optimization community, in particular truncated Newton methods (Nash [217] Schlick Overton [276] Schlick Fogelson [274] is given in a recent survey article by Schlick [273] For an adaptation of the truncated Newton optimization package TNPACK [274] to the molecular mechanics package CHARMM [33] see Derreumaux et al. 76] However, since the objective function has a huge number of local minima, a local optimization is likely to get stuck before the global minimum is reached. Thus some kind of global search is needed to find the global ....

T. Schlick and A. Fogelson, TNPACK -- A truncated Newton minimization package for large scale problems, ACM Trans. Math. Softw. 18 (1992), pp. 46--70, 71-111.

....of the TN code of Nash [16] is 325n flops per iteration. This cost is certainly higher than for limited memory variable metric methods, but we still expect it to be a small fraction of the total computing cost for many applications. The cost of the truncated Newton method of Schlick and Fogelson [19]) depends on OPTIMIZATION PROBLEMS ON PARALLEL ARCHITECTURES 13 Table 8.1 Evaluation of r 2 f(x)v (seconds) for the SSC problem on the CRAY 2 n t s t p 10,000 .18 .004 40,000 .70 .015 160,000 2.79 .061 640,000 11.20 .244 the preconditioner, so the situation is less clear with this code. ....

T. Schlick and A. Fogelson, TNPACK -- A truncated Newton minimization package for large-scale problems: I. Algorithms and usage, ACM Trans. Math. Software, 18 (1992), pp. 46--70.

....is described in Section 2, and the computation of the step in the trust region method is described in Section 3. Other codes that are suitable for the solution of large scale unconstrained minimization problems include LBFGS (Liu and Nocedal [15] TN (Nash [20] TNPACK (Folgeson and Schlick [26, 27]) SBMIN (Conn, Gould, and Toint [7, 6, 8] and STENMIN (Bouaricha [4, 5] LBFGS is a limited memory variable metric method, TN and TNPACK are truncated Newton methods, and STENMIN is a tensor code that bases each iteration on a tensor model of the objective function. Of these codes, only TN ....

T. Schlick and A. Fogelson, TNPACK -- A truncated Newton minimization package for large-scale problems: I. Algorithms and usage, ACM Trans. Math. Software, 18 (1992), pp. 46--70.

....and we want to satisfy (1) at least approximately, for the pairs in the data base. To make best use of current optimization technology, it is desirable to have a smooth (i.e. twice continuously differentiable with respect to x) potential. This allows for robust local optimization (e.g. [5,25]) and can be combined with global search techniques such as simulated annealing (e.g. 15,32] genetic algorithms (e.g. 10,31] smoothing methods (e.g. 21,16] or branch and bound techniques (e.g. 20] to approach the global minimizer for sequences s with unknown native geometry. ....

T. Schlick and A. Fogelson, TNPACK -- A truncated Newton minimization package for large scale problems, ACM Trans. Math. Softw. 18 (1992), 46-70; 71-111.

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T. Schlik and A. Fogelson, "TNPACK-A truncated Newton minimization package for large-scale problems: I. Algorithm and usage," ACM Transactions on Mathematical Software, vol. 18, no. 1, pp. 46--70, March 1992.

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T. Schlick, A. Fogelson, Tnpack: A truncated newton minimization package for large-scale problems: I. algorithm and usage, ACM Trans. on Math. Soft. 18 (1992) 46.

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Schlick, T. and A. Fogelson, 1992: TNPACK--A Truncated Newton minimization package for large-scale problems: II. Implementation examples. ACM Trans Math. Soft., 18 (1), 71-111.

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Schlick, T. and A. Fogelson, 1992: TNPACK--A truncated Newton minimization Package for large-scale problems: I. Algorithm and usage. ACM Trans on Math. Soft., 18 (1), 46-70.

No context found.

Schlick, T. and A. Fogelson, 1992: TNPACK--A Truncated Newton minimization package for large-scale problems: II. Implementation examples. ACM Trans Math. Soft., 18 (1), 71-111.

No context found.

Schlick, T. and A. Fogelson, 1992: TNPACK--A truncated Newton minimization Package for large-scale problems: I. Algorithm and usage. ACM Trans on Math. Soft., 18 (1), 46-70.

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Schlick, T. and A. Fogelson, 1992b: TNPACK--A Truncated Newton minimization package for large-scale problems: II. Implementation examples. ACMTOMS, 18 (1), 71-111.

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Schlick, T. and A. Fogelson, 1992a: TNPACK--A truncated Newton minimization Package for large-scale problems: I. Algorithm and usage. ACMTOMS, 18 (1), 46-70.

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