4,724 research outputs found
Separable Convex Optimization with Nested Lower and Upper Constraints
We study a convex resource allocation problem in which lower and upper bounds
are imposed on partial sums of allocations. This model is linked to a large
range of applications, including production planning, speed optimization,
stratified sampling, support vector machines, portfolio management, and
telecommunications. We propose an efficient gradient-free divide-and-conquer
algorithm, which uses monotonicity arguments to generate valid bounds from the
recursive calls, and eliminate linking constraints based on the information
from sub-problems. This algorithm does not need strict convexity or
differentiability. It produces an -approximate solution for the
continuous problem in time
and an integer solution in time, where is
the number of decision variables, is the number of constraints, and is
the resource bound. A complexity of is also achieved
for the linear and quadratic cases. These are the best complexities known to
date for this important problem class. Our experimental analyses confirm the
good performance of the method, which produces optimal solutions for problems
with up to 1,000,000 variables in a few seconds. Promising applications to the
support vector ordinal regression problem are also investigated
Energy-Efficient Scheduling and Power Allocation in Downlink OFDMA Networks with Base Station Coordination
This paper addresses the problem of energy-efficient resource allocation in
the downlink of a cellular OFDMA system. Three definitions of the energy
efficiency are considered for system design, accounting for both the radiated
and the circuit power. User scheduling and power allocation are optimized
across a cluster of coordinated base stations with a constraint on the maximum
transmit power (either per subcarrier or per base station). The asymptotic
noise-limited regime is discussed as a special case. %The performance of both
an isolated and a non-isolated cluster of coordinated base stations is examined
in the numerical experiments. Results show that the maximization of the energy
efficiency is approximately equivalent to the maximization of the spectral
efficiency for small values of the maximum transmit power, while there is a
wide range of values of the maximum transmit power for which a moderate
reduction of the data rate provides a large saving in terms of dissipated
energy. Also, the performance gap among the considered resource allocation
strategies reduces as the out-of-cluster interference increases.Comment: to appear on IEEE Transactions on Wireless Communication
Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers
We propose a solution strategy for a multimaterial minimum compliance
topology optimization problem, which consists in finding the optimal allocation
of a finite number of candidate (possibly anisotropic) materials inside a
reference domain, with the aim of maximizing the stiffness of the body. As a
relevant and novel application we consider the optimization of self-assembled
structures obtained by means of diblock copolymers. Such polymers are a class
of self-assembling materials which spontaneously synthesize periodic
microstructures at the nanoscale, whose anisotropic features can be exploited
to build structures with optimal elastic response, resembling biological
tissues exhibiting microstructures, such as bones and wood. For this purpose we
present a new generalization of the classical Optimality Criteria algorithm to
encompass a wider class of problems, where multiple candidate materials are
considered, the orientation of the anisotropic materials is optimized, and the
elastic properties of the materials are assumed to depend on a scalar
parameter, which is optimized simultaneously to the material allocation and
orientation. Well-posedness of the optimization problem and well-definition of
the presented algorithm are narrowly treated and proved. The capabilities of
the proposed method are assessed through several numerical tests
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