B. M. Averick and J. J. Mor'e. Evaluation of large-scale optimization problems on vector and parallel architectures. SIAM J. Optimization, 4:708--721, 1994. 28  Home/Search   Document Details and Download   Summary   Related Articles   Check

....reduction on distributedmemory machines or access to shared variables on shared memory machines. However, the updates for the gradient and the Hessian can be done efficiently by updating only the elements for which the corresponding elements of rf j and r 2 f j are non zeros (Averick and Mor e [7] and Mor e, Walenz, and Wu [63] The computation of the step, or its direction, with methods using the Hessian or Hessian approximations can be parallelized in several ways. In general, this is a place where a plug and play approach can be used by calling existing parallel linear algebra ....

B. M. Averick and J. J. Mor'e. Evaluation of large-scale optimization problems on vector and parallel architectures. SIAM J. Optimization, 4:708--721, 1994. 28

.... constraints but a large number of separable linear constraints was considered in [6] Some large scale y Department of Mathematics, Arizona State University, Tempe, AZ 85287 1804 problems with bound constraints were solved in [10] but none of these were included in the parallel version [1]. Frequently, parallelism is introduced for only part of the necessary computations as, for example, in [1] for the evaluation of function and gradient. A different approach is that of parallelization by problem decomposition as it was done in [12] This approach is in a way more appealing because ....

.... y Department of Mathematics, Arizona State University, Tempe, AZ 85287 1804 problems with bound constraints were solved in [10] but none of these were included in the parallel version [1] Frequently, parallelism is introduced for only part of the necessary computations as, for example, in [1] for the evaluation of function and gradient. A different approach is that of parallelization by problem decomposition as it was done in [12] This approach is in a way more appealing because it offers the possibility of continued use of welltested sequential algorithms and codes for the solution ....

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B.M. Averick and J.J. More, Evaluation of large-scale optimization problems on vector and parallel architectures, SIAM J. Optim. 4 (1994), 708--721.

....where T frf 0 (x) Deltag is the time required to compute the gradient of the partially separable function by a particular method. The above ratio can be expected for well coded gradient computations on scalar architectures but requires special techniques on vector and parallel architectures [2]. On vector architectures we can expect the ratio (5.1) to hold only if both the function and the gradient evaluation codes vectorize or if neither code vectorizes. An examination of Cray C90 results shows that only the MSA and ODC function evaluation codes fail to vectorize, and that the GL2 ....

B. M. Averick and J. J. Mor' e, Evaluation of large-scale optimization problems on vector and parallel architectures, SIAM J. Optimization, 4 (1994), pp. 708--721.

....by the user. The compact representation of H k permits the efficient computation of H k rf(x k ) in (8n v 1)n flops; all other operations in an iteration of the algorithm require 11n flops. We used the vmlm implementation of the limited memory variable metric algorithm (see Averick and Mor e [2]) which is based on the work of Liu and Nocedal [18] In all of our tests we used n v = 5. Instead of using a termination test, such as krf(x)k krf(x 0 )k; we terminate after 100 iterations. This strategy is needed because optimization algorithms that require many iterations for convergence ....

B. M. Averick and J. J. Mor' e, Evaluation of large-scale optimization problems on vector and parallel architectures, SIAM J. Optimization, 4 (1994), pp. 708--721.

....where T frf 0 (x) Deltag is the time required to compute the gradient of the partially separable function by a particular method. The above ratio can be expected for well coded gradient computations on scalar architectures but requires special techniques on vector and parallel architectures [2]. On vector architectures we can expect the ratio (14) to hold only if both the function and the gradient evaluation codes vectorize or if neither code vectorizes. An examination of Cray C90 results shows that only the MSA and ODC function evaluation codes fail to vectorize, and that the GL2 ....

AVERICK, B. and MOR ' E, J., 1994. Evaluation of large-scale optimization problems on vector and parallel architectures, SIAM Journal on Optimization 4, 708--721.

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