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341.
In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted?1(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems. 相似文献
342.
We estimate the kinematic measure of one convex domain moving to another under the groupG of rigid motions in
n
. We first estimate the kinematic formula for the total scalar curvature D
0gD
1
Rdv of then–2 dimensional intersection submanifold D
0gD
1. Then we use Chern and Yen's kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in
n
(4). Forn=4, we directly obtain another sufficient condition in 4. 相似文献
343.
This paper shows thatW
1,p
-quasiconvexity is a necessary and sufficient condition of swlsc (sw*lsc) for multiple integrals with a Caratheodory function as the variational function, bounded by
相似文献
344.
345.
346.
347.
We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2
4 – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2
4 –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R
g
2
>/<R
e
2
>=0.14026±0.00007, <R
m
2
>/<R
e
2
>=0.43961±0.00034, and *=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent
1=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for
1. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R
g
2
>/<R
e
2
>=0.1599±0.0002 and *=0.2471±0.0003; since *>0, hyperscaling holds. The approach to * is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2
4 – for two-dimensional SAWs. 相似文献
348.
349.
350.
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