38,900 research outputs found
Joint Scheduling and Resource Allocation in the OFDMA Downlink: Utility Maximization under Imperfect Channel-State Information
We consider the problem of simultaneous user-scheduling, power-allocation,
and rate-selection in an OFDMA downlink, with the goal of maximizing expected
sum-utility under a sum-power constraint. In doing so, we consider a family of
generic goodput-based utilities that facilitate, e.g., throughput-based
pricing, quality-of-service enforcement, and/or the treatment of practical
modulation-and-coding schemes (MCS). Since perfect knowledge of channel state
information (CSI) may be difficult to maintain at the base-station, especially
when the number of users and/or subchannels is large, we consider scheduling
and resource allocation under imperfect CSI, where the channel state is
described by a generic probability distribution. First, we consider the
"continuous" case where multiple users and/or code rates can time-share a
single OFDMA subchannel and time slot. This yields a non-convex optimization
problem that we convert into a convex optimization problem and solve exactly
using a dual optimization approach. Second, we consider the "discrete" case
where only a single user and code rate is allowed per OFDMA subchannel per time
slot. For the mixed-integer optimization problem that arises, we discuss the
connections it has with the continuous case and show that it can solved exactly
in some situations. For the other situations, we present a bound on the
optimality gap. For both cases, we provide algorithmic implementations of the
obtained solution. Finally, we study, numerically, the performance of the
proposed algorithms under various degrees of CSI uncertainty, utilities, and
OFDMA system configurations. In addition, we demonstrate advantages relative to
existing state-of-the-art algorithms
On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints
The problem of minimizing convex functionals of probability distributions is
solved under the assumption that the density of every distribution is bounded
from above and below. A system of sufficient and necessary first-order
optimality conditions as well as a bound on the optimality gap of feasible
candidate solutions are derived. Based on these results, two numerical
algorithms are proposed that iteratively solve the system of optimality
conditions on a grid of discrete points. Both algorithms use a block coordinate
descent strategy and terminate once the optimality gap falls below the desired
tolerance. While the first algorithm is conceptually simpler and more
efficient, it is not guaranteed to converge for objective functions that are
not strictly convex. This shortcoming is overcome in the second algorithm,
which uses an additional outer proximal iteration, and, which is proven to
converge under mild assumptions. Two examples are given to demonstrate the
theoretical usefulness of the optimality conditions as well as the high
efficiency and accuracy of the proposed numerical algorithms.Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on
Signal Processing. In previous versions, the example in Section VI.B
contained some mistakes and inaccuracies, which have been fixed in this
versio
The Optimal Uncertainty Algorithm in the Mystic Framework
We have recently proposed a rigorous framework for Uncertainty Quantification
(UQ) in which UQ objectives and assumption/information set are brought into the
forefront, providing a framework for the communication and comparison of UQ
results. In particular, this framework does not implicitly impose inappropriate
assumptions nor does it repudiate relevant information. This framework, which
we call Optimal Uncertainty Quantification (OUQ), is based on the observation
that given a set of assumptions and information, there exist bounds on
uncertainties obtained as values of optimization problems and that these bounds
are optimal. It provides a uniform environment for the optimal solution of the
problems of validation, certification, experimental design, reduced order
modeling, prediction, extrapolation, all under aleatoric and epistemic
uncertainties. OUQ optimization problems are extremely large, and even though
under general conditions they have finite-dimensional reductions, they must
often be solved numerically. This general algorithmic framework for OUQ has
been implemented in the mystic optimization framework. We describe this
implementation, and demonstrate its use in the context of the Caltech surrogate
model for hypervelocity impact
Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded
Decision trees usefully represent sparse, high dimensional and noisy data.
Having learned a function from this data, we may want to thereafter integrate
the function into a larger decision-making problem, e.g., for picking the best
chemical process catalyst. We study a large-scale, industrially-relevant
mixed-integer nonlinear nonconvex optimization problem involving both
gradient-boosted trees and penalty functions mitigating risk. This
mixed-integer optimization problem with convex penalty terms broadly applies to
optimizing pre-trained regression tree models. Decision makers may wish to
optimize discrete models to repurpose legacy predictive models, or they may
wish to optimize a discrete model that particularly well-represents a data set.
We develop several heuristic methods to find feasible solutions, and an exact,
branch-and-bound algorithm leveraging structural properties of the
gradient-boosted trees and penalty functions. We computationally test our
methods on concrete mixture design instance and a chemical catalysis industrial
instance
Algorithmic Superactivation of Asymptotic Quantum Capacity of Zero-Capacity Quantum Channels
The superactivation of zero-capacity quantum channels makes it possible to
use two zero-capacity quantum channels with a positive joint capacity for their
output. Currently, we have no theoretical background to describe all possible
combinations of superactive zero-capacity channels; hence, there may be many
other possible combinations. In practice, to discover such superactive
zero-capacity channel-pairs, we must analyze an extremely large set of possible
quantum states, channel models, and channel probabilities. There is still no
extremely efficient algorithmic tool for this purpose. This paper shows an
efficient algorithmical method of finding such combinations. Our method can be
a very valuable tool for improving the results of fault-tolerant quantum
computation and possible communication techniques over very noisy quantum
channels.Comment: 35 pages, 17 figures, Journal-ref: Information Sciences (Elsevier,
2012), presented in part at Quantum Information Processing 2012 (QIP2012),
v2: minor changes, v3: published version; Information Sciences, Elsevier,
ISSN: 0020-0255; 201
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