5,118 research outputs found
On angular momentum of gravitational radiation
The quasigroup approach to the conservation laws (Phys. Rev. D56, R7498
(1997)) is completed by imposing new gauge conditions for asymptotic
symmetries. Noether charge associated with an arbitrary element of the
Poincar\'e quasialgebra is free from the supertranslational ambiquity and
identically vanishes in a flat spacetimeComment: Revtex4 styl
Nonassociativity, Dirac monopoles and Aharonov-Bohm effect
The Aharonov-Bohm (AB) effect for the singular string associated with the
Dirac monopole carrying an arbitrary magnetic charge is studied. It is shown
that the emerging difficulties in explanation of the AB effect may be removed
by introducing nonassociative path-dependent wave functions. This provides the
absence of the AB effect for the Dirac string of magnetic monopole with an
arbitrary magnetic charge.Comment: Revised version. Typos corrected. References adde
Barrier subgradient method
In this paper we develop a new primal-dual subgradient method for nonsmooth convex optimization problems. This scheme is based on a self-concordant barrier for the basic feasible set. It is suitable for finding approximate solutions with certain relative accuracy. We discuss some applications of this technique including fractional covering problem, maximal concurrent flow problem, semidefinite relaxations and nonlinear online optimization.convex optimization, subgradient methods, non-smooth optimization, minimax problems, saddle points, variational inequalities, stochastic optimization, black-box methods, lower complexity bounds.
Smoothness parameter of power of Euclidean norm
In this paper, we study derivatives of powers of Euclidean norm. We prove
their H\"older continuity and establish explicit expressions for the
corresponding constants. We show that these constants are optimal for odd
derivatives and at most two times suboptimal for the even ones. In the
particular case of integer powers, when the H\"older continuity transforms into
the Lipschitz continuity, we improve this result and obtain the optimal
constants.Comment: J Optim Theory Appl (2020
Computationally efficient approximations of the joint spectral radius
The joint spectral radius of a set of matrices is a measure of the maximal
asymptotic growth rate that can be obtained by forming long products of
matrices taken from the set. This quantity appears in a number of application
contexts but is notoriously difficult to compute and to approximate. We
introduce in this paper a procedure for approximating the joint spectral radius
of a finite set of matrices with arbitrary high accuracy. Our approximation
procedure is polynomial in the size of the matrices once the number of matrices
and the desired accuracy are fixed
Tensor Methods for Minimizing Convex Functions with H\"{o}lder Continuous Higher-Order Derivatives
In this paper we study -order methods for unconstrained minimization of
convex functions that are -times differentiable () with
-H\"{o}lder continuous th derivatives. We propose tensor schemes with
and without acceleration. For the schemes without acceleration, we establish
iteration complexity bounds of
for reducing the functional
residual below a given . Assuming that is known, we
obtain an improved complexity bound of
for the corresponding
accelerated scheme. For the case in which is unknown, we present a
universal accelerated tensor scheme with iteration complexity of
. A lower complexity
bound of is also obtained
for this problem class.Comment: arXiv admin note: text overlap with arXiv:1907.0705
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