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Results for “Algorithmic Optimization”

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Fast optimization algorithms and the cosmological constant

Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of a problem that is hard for the complexity class NP (Nondeterministic Polynomial-time). The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable Universe. Here in this paper, we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10 -120 in a randomly generated 10 9 -dimensional Arkani-Hamed–Dimopoulos–Kachru landscape.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A 3D Voronoi+Gapper Galaxy Cluster Finder in Redshift Space to z ∼ 0.2 I: an Algorithm Optimized for the 2dFGRS

This paper is the first in a series, presenting a new galaxy cluster finder based on a three-dimensional Voronoi Tesselation plus a maximum likelihood estimator, followed by gapping-filtering in radial velocity(VoML+G). The scientific aim of the series is a reassessment of the diversity of optical clusters in the local universe. A mock galaxy database mimicking the southern strip of the magnitude(blue)-limited 2dF Galaxy Redshift Survey (2dFGRS), for the redshift range 0.009 < z < 0.22, is built on the basis of the Millennium Simulation of the LCDM cosmology and a reference catalog of “Millennium clusters,” spannning across the 1.0 × 10{sup 12}–1.0 × 10{sup 15} M {sub ⊙} h {sup −1} dark matter (DM) halo mass range, is recorded. The validation of VoML+G is performed through its application to the mock data and the ensuing determination of the completeness and purity of the cluster detections by comparison with the reference catalog. The execution of VoML+G over the 2dFGRS mock data identified 1614 clusters, 22% with N {sub g} ≥ 10, 64 percent with 10 > N {sub g} ≥ 5, and 14% with N {sub g} < 5. The ensemble of VoML+G clusters has a ∼59% completeness and a ∼66% purity, whereas the subsample with N {sub g} ≥ 10, to z ∼ 0.14, has greatly improved mean rates of ∼75% and ∼90%, respectively. The VoML+G cluster velocity dispersions are found to be compatible with those corresponding to “Millennium clusters” over the 300–1000 km s{sup −1} interval, i.e., for cluster halo masses in excess of ∼3.0 × 10{sup 13} M {sub ⊙} h {sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1973

A parallel variable metric optimization algorithm

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Straeter, T. A.↗