1,997 research outputs found
An SDP Approach For Solving Quadratic Fractional Programming Problems
This paper considers a fractional programming problem (P) which minimizes a
ratio of quadratic functions subject to a two-sided quadratic constraint. As is
well-known, the fractional objective function can be replaced by a parametric
family of quadratic functions, which makes (P) highly related to, but more
difficult than a single quadratic programming problem subject to a similar
constraint set. The task is to find the optimal parameter and then
look for the optimal solution if is attained. Contrasted with the
classical Dinkelbach method that iterates over the parameter, we propose a
suitable constraint qualification under which a new version of the S-lemma with
an equality can be proved so as to compute directly via an exact
SDP relaxation. When the constraint set of (P) is degenerated to become an
one-sided inequality, the same SDP approach can be applied to solve (P) {\it
without any condition}. We observe that the difference between a two-sided
problem and an one-sided problem lies in the fact that the S-lemma with an
equality does not have a natural Slater point to hold, which makes the former
essentially more difficult than the latter. This work does not, either, assume
the existence of a positive-definite linear combination of the quadratic terms
(also known as the dual Slater condition, or a positive-definite matrix
pencil), our result thus provides a novel extension to the so-called "hard
case" of the generalized trust region subproblem subject to the upper and the
lower level set of a quadratic function.Comment: 26 page
A Modified Levenberg-Marquardt Method for the Bidirectional Relay Channel
This paper presents an optimization approach for a system consisting of
multiple bidirectional links over a two-way amplify-and-forward relay. It is
desired to improve the fairness of the system. All user pairs exchange
information over one relay station with multiple antennas. Due to the joint
transmission to all users, the users are subject to mutual interference. A
mitigation of the interference can be achieved by max-min fair precoding
optimization where the relay is subject to a sum power constraint. The
resulting optimization problem is non-convex. This paper proposes a novel
iterative and low complexity approach based on a modified Levenberg-Marquardt
method to find near optimal solutions. The presented method finds solutions
close to the standard convex-solver based relaxation approach.Comment: submitted to IEEE Transactions on Vehicular Technology We corrected
small mistakes in the proof of Lemma 2 and Proposition
Blending Learning and Inference in Structured Prediction
In this paper we derive an efficient algorithm to learn the parameters of
structured predictors in general graphical models. This algorithm blends the
learning and inference tasks, which results in a significant speedup over
traditional approaches, such as conditional random fields and structured
support vector machines. For this purpose we utilize the structures of the
predictors to describe a low dimensional structured prediction task which
encourages local consistencies within the different structures while learning
the parameters of the model. Convexity of the learning task provides the means
to enforce the consistencies between the different parts. The
inference-learning blending algorithm that we propose is guaranteed to converge
to the optimum of the low dimensional primal and dual programs. Unlike many of
the existing approaches, the inference-learning blending allows us to learn
efficiently high-order graphical models, over regions of any size, and very
large number of parameters. We demonstrate the effectiveness of our approach,
while presenting state-of-the-art results in stereo estimation, semantic
segmentation, shape reconstruction, and indoor scene understanding
A Practical Guide to Robust Optimization
Robust optimization is a young and active research field that has been mainly
developed in the last 15 years. Robust optimization is very useful for
practice, since it is tailored to the information at hand, and it leads to
computationally tractable formulations. It is therefore remarkable that
real-life applications of robust optimization are still lagging behind; there
is much more potential for real-life applications than has been exploited
hitherto. The aim of this paper is to help practitioners to understand robust
optimization and to successfully apply it in practice. We provide a brief
introduction to robust optimization, and also describe important do's and
don'ts for using it in practice. We use many small examples to illustrate our
discussions
Conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone
We investigate the completely positive semidefinite cone ,
a new matrix cone consisting of all matrices that admit a Gram
representation by positive semidefinite matrices (of any size). In particular
we study relationships between this cone and the completely positive and doubly
nonnegative cones, and between its dual cone and trace positive non-commutative
polynomials.
We use this new cone to model quantum analogues of the classical independence
and chromatic graph parameters and , which are roughly
obtained by allowing variables to be positive semidefinite matrices instead of
scalars in the programs defining the classical parameters. We can
formulate these quantum parameters as conic linear programs over the cone
. Using this conic approach we can recover the bounds in
terms of the theta number and define further approximations by exploiting the
link to trace positive polynomials.Comment: Fixed some typo
Applications of quark-hadron duality in F2 structure function
Inclusive electron-proton and electron-deuteron inelastic cross sections have
been measured at Jefferson Lab (JLab) in the resonance region, at large Bjorken
x, up to 0.92, and four-momentum transfer squared Q2 up to 7.5 GeV2 in the
experiment E00-116. These measurements are used to extend to larger x and Q2
precision, quantitative, studies of the phenomenon of quark-hadron duality. Our
analysis confirms, both globally and locally, the apparent violation of
quark-hadron duality previously observed at a Q2 of 3.5 GeV2 when resonance
data are compared to structure function data created from CTEQ6M and MRST2004
parton distribution functions (PDFs). More importantly, our new data show that
this discrepancy saturates by Q2 ~ 4 Gev2, becoming Q2 independent. This
suggests only small violations of Q2 evolution by contributions from the
higher-twist terms in the resonance region which is confirmed by our
comparisons to ALEKHIN and ALLM97.We conclude that the unconstrained strength
of the CTEQ6M and MRST2004 PDFs at large x is the major source of the
disagreement between data and these parameterizations in the kinematic regime
we study and that, in view of quark-hadron duality, properly averaged resonance
region data could be used in global QCD fits to reduce PDF uncertainties at
large x.Comment: 35 page
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