1,679 research outputs found
Second-order subdifferential calculus with applications to tilt stability in optimization
The paper concerns the second-order generalized differentiation theory of
variational analysis and new applications of this theory to some problems of
constrained optimization in finitedimensional spaces. The main attention is
paid to the so-called (full and partial) second-order subdifferentials of
extended-real-valued functions, which are dual-type constructions generated by
coderivatives of frst-order subdifferential mappings. We develop an extended
second-order subdifferential calculus and analyze the basic second-order
qualification condition ensuring the fulfillment of the principal secondorder
chain rule for strongly and fully amenable compositions. The calculus results
obtained in this way and computing the second-order subdifferentials for
piecewise linear-quadratic functions and their major specifications are applied
then to the study of tilt stability of local minimizers for important classes
of problems in constrained optimization that include, in particular, problems
of nonlinear programming and certain classes of extended nonlinear programs
described in composite terms
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment
A procedure is described for efficiently finding the ground state energy and
configuration for a Frenkel-Kontorova model in a periodic potential, consisting
of N parabolic segments of identical curvature in each period, through a
numerical solution of the convex minimization problem described in the
preceding paper. The key elements are the use of subdifferentials to describe
the structure of the minimization problem; an intuitive picture of how to solve
it, based on motion of quasiparticles; and a fast linear optimization method
with a reduced memory requirement. The procedure has been tested for N up to
200.Comment: 9 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 3 Postscript
figures, accepted by Phys.Rev.B to be published together with
cond-mat/970722
Numerical Analysis of the Capacities for Two-Qubit Unitary Operations
We present numerical results on the capacities of two-qubit unitary
operations for creating entanglement and increasing the Holevo information of
an ensemble. In all cases tested, the maximum values calculated for the
capacities based on the Holevo information are close to the capacities based on
the entanglement. This indicates that the capacities based on the Holevo
information, which are very difficult to calculate, may be estimated from the
capacities based upon the entanglement, which are relatively straightforward to
calculate.Comment: 9 pages, 10 figure
Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems
We give a description of the level sets in the higher dimensional
multifractal formalism for infinite conformal graph directed Markov systems. If
these systems possess a certain degree of regularity this description is
complete in the sense that we identify all values with non-empty level sets and
determine their Hausdorff dimension. This result is also partially new for the
finite alphabet case.Comment: 20 pages, 1 figur
Minimum L1-distance projection onto the boundary of a convex set: Simple characterization
We show that the minimum distance projection in the L1-norm from an interior
point onto the boundary of a convex set is achieved by a single, unidimensional
projection. Application of this characterization when the convex set is a
polyhedron leads to either an elementary minmax problem or a set of easily
solved linear programs, depending upon whether the polyhedron is given as the
intersection of a set of half spaces or as the convex hull of a set of extreme
points. The outcome is an easier and more straightforward derivation of the
special case results given in a recent paper by Briec.Comment: 5 page
Non-Bilocal Measurement via Entangled State
Two observers, who share a pair of particles in an entangled mixed state, can
use it to perform some non-bilocal measurement over another bipartite system.
In particular, one can construct a specific game played by the observers
against a coordinator, in which they can score better than a pair of observers
who only share a classical communication channel.Comment: 6 pages. minor change
Detecting separable states via semidefinite programs
We introduce a new technique to detect separable states using semidefinite
programs. This approach provides a sufficient condition for separability of a
state that is based on the existence of a certain local linear map applied to a
known separable state. When a state is shown to be separable, a proof of this
fact is provided in the form of an explicit convex decomposition of the state
in terms of product states. All states in the interior of the set of separable
states can be detected in this way, except maybe for a set of measure zero.
Even though this technique is more suited for a numerical approach, a new
analytical criterion for separability can also be derived.Comment: 8 pages, accepted for publication in Physical Review
Estimating entanglement measures in experiments
We present a method to estimate entanglement measures in experiments. We show
how a lower bound on a generic entanglement measure can be derived from the
measured expectation values of any finite collection of entanglement witnesses.
Hence witness measurements are given a quantitative meaning without the need of
further experimental data. We apply our results to a recent multi-photon
experiment [M. Bourennane et al., Phys. Rev. Lett. 92, 087902 (2004)], giving
bounds on the entanglement of formation and the geometric measure of
entanglement in this experiment.Comment: 4 pages, 1 figure, v2: final versio
On the tensor convolution and the quantum separability problem
We consider the problem of separability: decide whether a Hermitian operator
on a finite dimensional Hilbert tensor product is separable or entangled. We
show that the tensor convolution defined for certain mappings on an almost
arbitrary locally compact abelian group, give rise to formulation of an
equivalent problem to the separability one.Comment: 13 pages, two sections adde
Methods for calculating nonconcave entropies
Five different methods which can be used to analytically calculate entropies
that are nonconcave as functions of the energy in the thermodynamic limit are
discussed and compared. The five methods are based on the following ideas and
techniques: i) microcanonical contraction, ii) metastable branches of the free
energy, iii) generalized canonical ensembles with specific illustrations
involving the so-called Gaussian and Betrag ensembles, iv) restricted canonical
ensemble, and v) inverse Laplace transform. A simple long-range spin model
having a nonconcave entropy is used to illustrate each method.Comment: v1: 22 pages, IOP style, 7 color figures, contribution for the JSTAT
special issue on Long-range interacting systems. v2: Open problem and
references added, minor typos corrected, close to published versio
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