, A Fortran-90 based multiprecision system, ACM Trans. Math. Softw., 21 (1995), pp. 379--387.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that is, f can be written as f(x) n f X i=1 f i (x) where each element function f i only depends on a few components of x, and n f is the number of element functions. Algorithms and software that take advantage of partial separability have been developed for various problems (for example, [23, 24, 25, 26, 9]) but this software requires that the user provide the gradient of f and the partial separability structure (a list of the dependent variables for each element function f i ) The NEOS solvers for partially separable problems require that the user specify the number of variables n, a subroutine ....

, LSNNO: A Fortran subroutine for solving large-scale nonlinear network optimization problems, ACM Trans. Math. Software, 18 (1992), pp. 308--328.

....Algorithm 1 above when d is odd and with [11, Algorithm 1] when d is even. 5. Experimental Results We programmed Algorithm 1 in Fortran 90 in the same interval arithmetic environment and on the same machine as the experiments in [13] and [11] Namely, we used the Fortran 90 system described in [9] and [10] with subsequent improvements within the GlobSol project [3] and we used the Sun Fortran 95 compiler version 6.0 with optimization level 0 on a Sparc Ultra 1 model 140. We tested Algorithm 1 above with Example 2 from [11] that is, with Example 5.1 (Example 2 from [11] motivated from ....

, A Fortran 90 environment for research and prototyping of enclosure algorithms for nonlinear equations and global optimization, ACM Trans. Math. Software 21 (1995), no. 1, 63-78.

....be implemented in a process similar to automatic differentiation, so the user need only program the function itself. The review [32] contains tips on how to do this efficiently and with small output intervals; we have implemented such slope computations as a subroutine in our Fortran 90 system of [13]. 3 e.g. that natural interval extension obtained by a given form of automatic differentiation and evaluation with interval arithmetic 6 R. B. Kearfott Obtaining X a and W involves a process termed ffl inflation, originated by Rump in [31] and further described by Mayer, e.g. in [22] This ....

....using Horner s scheme wherever possible, although this does not always result in optimal bounds on ranges. Our actual Fortran 90 subroutines are available upon request. 7.2. The Implementation Environment. The algorithm was implemented within the research and prototyping environment described in [13]. This environment has an interval data type that uses the routines in INTLIB ( 14] as well as dynamically allocated linked lists of boxes. The problems are input as expressions, loops and subroutines in Fortran syntax, and an internal representation is then generated. This single internal ....

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, A Fortran 90 environment for research and prototyping of enclosure algorithms for nonlinear equations and global optimization, ACM Trans. Math. Software, 21 (1995), pp. 63--78.

....large scale optimization problems since, as shown by Griewank and Toint, a function f 0 is partially separable if the Hessian matrix r 2 f 0 (x) is sparse. Algorithms and software that take advantage of the partially separable structure have been developed for various problems. See, for example, [27, 14, 23, 31, 32, 33, 34]. In these algorithms the partially separable structure is used mainly to approximate the (dense) Hessian matrices r 2 f i (x) by quasi Newton methods. Partial separability is also used to compute the gradient of f 0 as the sum of the gradients of the element functions f i , but this is just ....

, LSNNO: A Fortran subroutine for solving large-scale nonlinear network optimization problems, ACM Trans. Math. Software, 18 (1992), pp. 308--328.

....is, f 0 can be written as f 0 (x) m X i=1 f i (x) 1:2) where each element function f i depends only on a few components of x, and m is the number of element functions. Algorithms and software that take advantage of partial separability have been developed for various problems (for example, [14, 19, 20, 17, 21, 22, 10]) but this software requires that the user provide the gradient of f 0 . An important design goal of ELSO is to avoid this requirement. For small scale problems we can approximate the gradient by differences of function values, for example, rf 0 (x) i f 0 (x h i e i ) Gamma f 0 (x) h i ....

, LSNNO: A Fortran subroutine for solving large-scale nonlinear network optimization problems, ACM Trans. Math. Software, 18 (1992), pp. 308--328.

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, A Fortran-90 based multiprecision system, ACM Trans. Math. Softw., 21 (1995), pp. 379--387.

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FORTRAN Basic Linear Algebra Subprograms. ACM Trans. Math. Soft., 14#1#:1#17, March 1988.

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Fortran usage. ACM Trans. Math. Softw., 5:308#323, 1979.

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FORTRAN Basic Linear Algebra Subprograms. ACM Trans. Math. Software, 14:1#32, 399, 1988. #Algorithm 656#.

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