An efficient method for finding the minimum of a function of several variables without calculating derivatives

Powell, M. J. D.

doi:10.1093/comjnl/7.2.155

Cited by 4,005 publications

(1,537 citation statements)

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“…For Al 55 , the results show an expansion of the jellium. We notice that even though the surface region in this case is contracted (∆r s 2 † =-0.068), the expansion of the inner region (∆r s 1 † =+0.206) is dominated and resulted in an overall expansion.…”

Section: B Sc-isjm Resultsmentioning

confidence: 88%

“…The calculations then are repeated for different points in the {n 1 ,n 2 } parameter space (keeping the number of atoms in each region as fixed) until a local minimum is achieved. 55 The global minimum-energy state is then selected from the calculated local-minimum states for different t values, and thereby the equilibrium value, t † , is singled out. For t we arbitrarily use the values obtained from t = νd 100 in which ν takes positive integer values and d 100 is the distance between two adjacent (100) planes, being 3.82, 4.05, and 5.72 for Al, Na, and Cs, respectively.…”

Section: A Sc-isjmmentioning

confidence: 99%

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Density-functional theory study of ionic inhomogeneity in metal clusters using SC-ISJM

Payami

Mahmoodi

2017

Surface Science

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In this work we have applied the recently formulated self-compressed inhomogeneous stabilized jellium model [M. Payami and T. Mahmoodi, Can. J. Phys. 89, 967 (2011)] to describe the equilibrium electronic and geometric properties of atomic-closed-shell simple metal clusters of AlN (N =13, 19, 43, 55, 79, 87, 135, 141), NaN , and CsN (N =9,15,27,51, 59, 65, 89, 113). To validate the results, we have also performed first-principles pseudo-potential calculations and used them as our reference. In the model, we have considered two regions consisting of "surface" and "inner" ones, the border separating them is sharp. This generalization makes possible to decouple the relaxations of different parts of the system. The results show that the present model correctly predicts the size reductions seen in most of the clusters. It also predicts increase in size of some clusters, as observed from first-principles results. The other property is the change of inter-layer distances, which in most cases were realized as contractions and in a few cases as expansions, are reproduced in good agreement with the atomic simulation results. For a better description of the properties, it is possible to improve the method of choosing the thicknesses or generalize the model to include more regions than just two.

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Section: B Sc-isjm Resultsmentioning

confidence: 88%

Section: A Sc-isjmmentioning

confidence: 99%

Density-functional theory study of ionic inhomogeneity in metal clusters using SC-ISJM

Payami

Mahmoodi

2017

Surface Science

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“…We adopt the same likelihood function for RV modeling as Howard et al (2014): Powell (1964) to find the maximum likelihood model. Fifty parallel MCMC chains ("walkers") are then initialized by perturbing each of the free parameters from the maximum likelihood values by as much as 3%.…”

Section: Light-curve Analysismentioning

confidence: 99%

K2-66b and K2-106b: Two Extremely Hot Sub-Neptune-size Planets with High Densities

Sinukoff

Howard

Petigura

et al. 2017

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We report precise mass and density measurements of two extremely hot sub-Neptune-size planets from the K2 mission using radial velocities, K2 photometry, and adaptive optics imaging. K2-66 harbors a close-in subNeptune-sized ( -+ 2.49 0.24 0.34 Å R ) planet (K2-66b) with a mass of  21.3 3.6 Å M . Because the star is evolving up the subgiant branch, K2-66b receives a high level of irradiation, roughly twice the main-sequence value. K2-66b may reside within the so-called "photoevaporation desert," a domain of planet size and incident flux that is almost completely devoid of planets. Its mass and radius imply that K2-66b has, at most, a meager envelope fraction (<5%) and perhaps no envelope at all, making it one of the largest planets without a significant envelope. K2-106 hosts an ultra-short-period planet (P=13.7 hr) that is one of the hottest sub-Neptune-size planets discovered to date. Its radius ( -+ 1.82 0.14 0.20 Å R ) and mass (  9.0 1.6 Å M ) are consistent with a rocky composition, as are all other small ultra-short-period planets with well-measured masses. K2-106 also hosts a larger, longer-period planet (R p = -+ 2.77 0.23 0.37 Å R , P=13.3 days) with a mass less than 24.4 Å M at 99.7% confidence. K2-66b and K2-106b probe planetary physics in extreme radiation environments. Their high densities reflect the challenge of retaining a substantial gas envelope in such extreme environments.

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“…In order to solve the ND unconstrained optimization subproblem, we use Powell's conjugate direction method [17] as it requires only the objective function value and is more robust to noise in function evaluation, which is often the case with image based objective functions. For 1D optimization subproblem we employ Golden section with Swann's bounding [18].…”

Section: Convex Optimizationmentioning

confidence: 99%

An Optimization Based Framework for Human Pose Estimation in Monocular Videos

Agarwal

Kumar

Ryde

et al. 2012

Advances in Visual Computing

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Abstract. Human pose estimation using monocular vision is a challenging problem in computer vision. Past work has focused on developing efficient inference algorithms and probabilistic prior models based on captured kinematic/dynamic measurements. However, such algorithms face challenges in generalization beyond the learned dataset. In this work, we propose a model-based generative approach for estimating the human pose solely from uncalibrated monocular video in unconstrained environments without any prior learning on motion capture/image annotation data. We propose a novel Product of Heading Experts (PoHE) based generalized heading estimation framework by probabilistically-merging heading outputs (probabilistic/ non-probabilistic) from time varying number of estimators to bootstrap a synergistically integrated probabilistic-deterministic sequential optimization framework for robustly estimating human pose. Novel pixel-distance based performance measures are developed to penalize false human detections and ensure identity-maintained human tracking. We tested our framework with varied inputs (silhouette and bounding boxes) to evaluate, compare and benchmark it against ground-truth data (collected using our human annotation tool) for 52 video vignettes in the publicly available DARPA Mind's Eye Year I dataset 1 . Results show robust pose estimates on this challenging dataset of highly diverse activities.

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An efficient method for finding the minimum of a function of several variables without calculating derivatives

Cited by 4,005 publications

References 0 publications

Density-functional theory study of ionic inhomogeneity in metal clusters using SC-ISJM

Density-functional theory study of ionic inhomogeneity in metal clusters using SC-ISJM

K2-66b and K2-106b: Two Extremely Hot Sub-Neptune-size Planets with High Densities

An Optimization Based Framework for Human Pose Estimation in Monocular Videos

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