4,724 research outputs found

    Separable Convex Optimization with Nested Lower and Upper Constraints

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    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 ϵ\epsilon-approximate solution for the continuous problem in O(nlogmlognBϵ)\mathcal{O}(n \log m \log \frac{n B}{\epsilon}) time and an integer solution in O(nlogmlogB)\mathcal{O}(n \log m \log B) time, where nn is the number of decision variables, mm is the number of constraints, and BB is the resource bound. A complexity of O(nlogm)\mathcal{O}(n \log m) 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

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    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

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    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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