5,900 research outputs found
Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems
We consider projection algorithms for solving (nonconvex) feasibility
problems in Euclidean spaces. Of special interest are the Method of Alternating
Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection
Algorithm (AAR). In the case of convex feasibility, firm nonexpansiveness of
projection mappings is a global property that yields global convergence of MAP
and for consistent problems AAR. Based on (\epsilon, \delta)-regularity of sets
developed by Bauschke, Luke, Phan and Wang in 2012, a relaxed local version of
firm nonexpansiveness with respect to the intersection is introduced for
consistent feasibility problems. Together with a coercivity condition that
relates to the regularity of the intersection, this yields local linear
convergence of MAP for a wide class of nonconvex problems,Comment: 22 pages, no figures, 30 reference
Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
The problem of finding a vector with the fewest nonzero elements that
satisfies an underdetermined system of linear equations is an NP-complete
problem that is typically solved numerically via convex heuristics or
nicely-behaved nonconvex relaxations. In this work we consider elementary
methods based on projections for solving a sparse feasibility problem without
employing convex heuristics. In a recent paper Bauschke, Luke, Phan and Wang
(2014) showed that, locally, the fundamental method of alternating projections
must converge linearly to a solution to the sparse feasibility problem with an
affine constraint. In this paper we apply different analytical tools that allow
us to show global linear convergence of alternating projections under familiar
constraint qualifications. These analytical tools can also be applied to other
algorithms. This is demonstrated with the prominent Douglas-Rachford algorithm
where we establish local linear convergence of this method applied to the
sparse affine feasibility problem.Comment: 29 pages, 2 figures, 37 references. Much expanded version from last
submission. Title changed to reflect new development
Magnetic Properties of Pr0.7Ca0.3MnO3/SrRuO3 Superlattices
High-quality Pr0.7Ca0.3MnO3/SrRuO3 superlattices were fabricated by pulsed
laser deposition and were investigated by high-resolution transmission electron
microscopy and SQUID magnetometry. Superlattices with orthorhombic and
tetragonal SrRuO3 layers were investigated. The superlattices grew coherently;
in the growth direction Pr0.7Ca0.3MnO3 layers were terminated by MnO2- and
SrRuO3 layers by RuO2-planes. All superlattices showed antiferromagnetic
interlayer coupling in low magnetic fields. The coupling strength was
significantly higher for orthorhombic than for tetragonal symmetry of the
SrRuO3 layers. The strong interlayer exchange coupling in the superlattice with
orthorhombic SrRuO3 layers led to a magnetization reversal mechanism with a
partially inverted hysteresis loop.Comment: 12 pages, 4 figure
Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness
Convex optimization has become ubiquitous in most quantitative disciplines of
science, including variational image processing. Proximal splitting algorithms
are becoming popular to solve such structured convex optimization problems.
Within this class of algorithms, Douglas--Rachford (DR) and alternating
direction method of multipliers (ADMM) are designed to minimize the sum of two
proper lower semi-continuous convex functions whose proximity operators are
easy to compute. The goal of this work is to understand the local convergence
behaviour of DR (resp. ADMM) when the involved functions (resp. their
Legendre-Fenchel conjugates) are moreover partly smooth. More precisely, when
both of the two functions (resp. their conjugates) are partly smooth relative
to their respective manifolds, we show that DR (resp. ADMM) identifies these
manifolds in finite time. Moreover, when these manifolds are affine or linear,
we prove that DR/ADMM is locally linearly convergent. When and are
locally polyhedral, we show that the optimal convergence radius is given in
terms of the cosine of the Friedrichs angle between the tangent spaces of the
identified manifolds. This is illustrated by several concrete examples and
supported by numerical experiments.Comment: 17 pages, 1 figure, published in the proceedings of the Fifth
International Conference on Scale Space and Variational Methods in Computer
Visio
The INTEGRAL-OMC Scientific Archive
The Optical Monitoring Camera (OMC) on-board the INTEGRAL satellite has, as
one of its scientific goals, the observation of a large number of variable
sources previously selected. After almost 6 years of operations, OMC has
monitored more than 100 000 sources of scientific interest. In this
contribution we present the OMC Scientific Archive
(http://sdc.laeff.inta.es/omc/) which has been developed to provide the
astronomical community with a quick access to the light curves generated by
this instrument.We describe the main characteristics of this archive, as well
as important aspects for the users: object types, temporal sampling of light
curves and photometric accuracy.Comment: 4 pages, 5 figures. "Highlights of Spanish Astrophysics V"
Proceedings of the VIII Scientific Meeting of the Spanish Astronomical
Society (SEA) held in Santander, July 7-11, 200
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