By Almerico Murli, Gerardo Toraldo
Computational matters in excessive functionality software program for Nonlinear Research brings jointly in a single position very important contributions and up to date learn ends up in this significant quarter.
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For all k 2 0. Let be any closed, bounded set containing the iterates dlC) We shall follow the outline given above. (i) Status of the starting point. 4);moreover, ge(x*,A*), = 0 for all j E F1 and x: > 0 for all j E 3; nn/b and x*3 = 0 and ge(z*, A*)j > 0 for all i E D1. (65) 56 CONN. (x, A)j) converges to zero while its partner converges to a strictly positive limit for each j E & (assumption AS7), we may define nontrivial regions which separate the two sequences for all k sufficiently large. Let *f Ex - 8 1 + 8 min max[x;, ge(x*,A*)j] j € N b > 0, where 8 is as in (32).
The justification of this remark comes about by noting that the compressed AD approach works provided the sparsity pattern of the Jacobian matrix f’(z)is a subset of the sparsity pattern provided by the user. Of course, if the sparsity pattern provided by the user is too large, then the number of groups p is likely to increase, leading to increased memory requirements and some loss in efficiency in the computation of the gradient. IMPACT O F PARTIAL SEPARABILITY ON LARGE-SCALE OPTIRiIIZATION 33 Table 1.
J. Mor6, and G-L. Xue. The MINPACK-2 test problem collection. Preprint MCS-PI 53-0692, Mathematics and Computer Science Division, Argonne National Laboratory, 1992. B. M. Averick and J. J. More. Evaluation of large-scale optimization problems on vector and parallel architectures. SIAM J. Optimization, 4:708-72 1, 1994. Christian Bischof, Ali Bouaricha, Peyvand Kahdemi, and Jorge J. Mork. Computing gradients in large-scale optimization using automatic differentiation. Preprint MCS-P488-0 195, Argonne National Laboratory, Argonne, Illinois, 1995.