For a proof of the monotone column permanent (MCP) conjecture for dimension 4 it is sufficient to show that 4 polynomials, which come from the permanents of real matrices, are nonnegative for all real values of the va...
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ISBN:
(纸本)9781605586649
For a proof of the monotone column permanent (MCP) conjecture for dimension 4 it is sufficient to show that 4 polynomials, which come from the permanents of real matrices, are nonnegative for all real values of the variables, where the degrees and the number of the variables of these polynomials are all 8. Here we apply a hybrid symbolic-numerical algorithm for certifying that these polynomials can be written as an exact fraction of two polynomial sums -of-squares (SOS) with rational coefficients.
We propose a convex optimization method for maximum likelihood estimation of autoregressive models, subject to conditional independence constraints. This problem is an extension to times series of the classical covari...
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ISBN:
(纸本)9781424423538
We propose a convex optimization method for maximum likelihood estimation of autoregressive models, subject to conditional independence constraints. This problem is an extension to times series of the classical covariance selection problem in graphical modeling. The conditional independence constraints impose quadratic equalities on the autoregressive model parameters, which makes the maximum likelihood estimation problem nonconvex and difficult to solve. We formulate a convex relaxation and prove that it is exact when the sample covariance matrix is block-Toeplitz. We also observe experimentally that in practice the relaxation is exact under much weaker conditions. We discuss applications to topology selection in graphical models of time series, by enumerating all possible topologies, and ranking them using information-theoretic model selection criteria. The method is illustrated by an example of air pollution data.
This paper deals with robust adaptive detection of a useful target in the presence of interfering signals. The background environment is assumed homogeneous and Gaussian with unknown covariance matrix. At the design s...
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ISBN:
(纸本)9780819478139
This paper deals with robust adaptive detection of a useful target in the presence of interfering signals. The background environment is assumed homogeneous and Gaussian with unknown covariance matrix. At the design stage, we devise a robust receiver with angular rejection capabilities, accounting for covariance and steering uncertainties. We prove that the maximization of the concentrated likelihood function shares a hidden convexity property. Specifically, exploiting some recent results concerning trigonometric polynomials, we formulate the apparently non-convex optimization over the phase as a semidefinite programming convex optimization problem. At the analysis stage, we assess the performance of the new receiver in comparison with classic detectors available in open literature.
We study the impact of user association policies on flow-level performance in interference limited wireless networks. Most research in this area has used static interference models (neighboring base stations are alway...
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ISBN:
(纸本)9783642104053
We study the impact of user association policies on flow-level performance in interference limited wireless networks. Most research in this area has used static interference models (neighboring base stations are always active) and resorted to intuitive objectives such as load balancing. In this paper, we show that this can be counterproductive in the presence of dynamic interference which couples the transmission rates to users at various base stations. We propose a methodology to optimize the performance of a class of coupled systems, and apply it to study the user association problem. We show that by properly inducing load asymmetries, substantial performance gains can be achieved relative to a load balancing policy (e.g., 15 times reduction in mean delay). Systematic simulations establish that our optimized static policy substantially outperforms various dynamic policies and that these results are robust to changes in file size distributions, channel parameters, and spatial load distributions.
We address ranging energy optimization for an unsynchronized localization system, which features robust sensor positioning, in the sense that specific accuracy requirements are fulfilled within a prescribed service ar...
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ISBN:
(纸本)9781424423538
We address ranging energy optimization for an unsynchronized localization system, which features robust sensor positioning, in the sense that specific accuracy requirements are fulfilled within a prescribed service area. Optimization problems related to the ranging energy of a sensor and beacons are proposed, after which a practical algorithm based on semidefinite programming is presented. The effectiveness of the algorithm is illustrated by a numerical experiment.
We study integrality gaps for SDP relaxations of constraint satisfaction problems, in the hierarchy of SDPs defilled by Lasserre. Schoenebeck [23] recently showed the first integrality gaps for these problems, showing...
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ISBN:
(纸本)9781605586137
We study integrality gaps for SDP relaxations of constraint satisfaction problems, in the hierarchy of SDPs defilled by Lasserre. Schoenebeck [23] recently showed the first integrality gaps for these problems, showing that, for MAX k-XOR, the ratio of the SDP optimum to the integer opthimum may be as large as 2 even after Omega(n) rounds of the Lasserre hierarchy . We show that for the general MAX k-CSP problem, this ratio can be as large as 2(k)/2k - epsilon, when the alphabet is binary and q(k)/q(q - 1)k - epsilon when the alphabet size a prime q, even after Omega(n) rounds of the Lasserre hierarchy. We also explore how to translate gaps for CSP into integrality gaps for other problems using reductions, and establish SDP gaps for Maximum Independent Set, Approximate Graph Coloring, Chromatic Number and Minimum Vertex Cover. For Independent Set. and Chromatic Number, we show integrality gaps of n/2(O(root log n log log n)) even after 2(Omega(root log n log log n)) rounds. In case of Approximate Graph Coloring, for every constant we Construct graphs with chromatic number Omega(2(1/2) /l(2)), which admit a a vector l-coloring for the SDP obtained by Omega(n) rounds. For Vertex Cover, we show an integrality all of 1.36 for Omega(n(delta)) rounds, for a small constant delta. The results for CSPs provide the first examples of Omega(n) round integrality gaps matching hardness results known only, under Unique Games Conjecture. This and some additional properties of the integrality gap instance, allow for gaps for in case of Independent Set and Chromatic Number which are stronger than the NP-hardness results known even under the Unique Games Conjecture.
We consider the problem of maximum likelihood (ML) signal detection in multiple-input multiple-output (MIMO) wireless communication systems. We propose a new preprocessing algorithm in the form of channel ordering for...
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ISBN:
(纸本)9781424441471
We consider the problem of maximum likelihood (ML) signal detection in multiple-input multiple-output (MIMO) wireless communication systems. We propose a new preprocessing algorithm in the form of channel ordering for sphere decoders. Numerical results show that this new channel ordering leads to significantly lower complexity (in the form of the number of nodes visited by the search algorithm);for MPSK modulation where M >= 8 and a moderate SNR range of 15 - 24 dB, our channel ordering results in a two-fold to four-fold decrease in the number of nodes visited by the search algorithm. We also present a brief review of the SDR-ML detector, formulated using semidefinite programming and relaxation techniques. Finally, we propose a combined SDR-ML-sphere decoder and demonstrate that it further reduces the number of nodes visited by the search algorithm;for a 20 x 20 BPSK-modulated MIMO system and SNR of 8 dB, the SDR-ML-sphere decoder has an average complexity that is approximately 5 times less than the sphere decoder.
A unified framework to jointly solve the problems of localization and synchronization at the same time is presented in this paper. The joint approach is attractive because it can solve both localization and synchroniz...
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ISBN:
(纸本)9781424423538
A unified framework to jointly solve the problems of localization and synchronization at the same time is presented in this paper. The joint approach is attractive because it can solve both localization and synchronization using the same set of message exchanges, which is extremely important for energy saving in wireless sensor networks. The inaccuracy of anchor locations and timings is taken into account to provide accurate joint localization and synchronization. The anchor uncertainties are assumed to be bounded, but knowledge of the statistics of anchor uncertainties is not required. The problem is formulated into a linear model with uncertainties on both sides of the equation. A robust joint estimator is then proposed based on minimizing the worst-case mean square error and the solution is obtained by solving a semidefinite programming problem. Simulation results show that the proposed estimator outperforms the traditional least squares estimator at the cost of higher computational complexity.
The problem under study here is the minimax design of linear-phase lowpass FIR filters having variable passband width and implemented through a Farrow structure. We have two main contributions. The first is the design...
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ISBN:
(纸本)9781424423538
The problem under study here is the minimax design of linear-phase lowpass FIR filters having variable passband width and implemented through a Farrow structure. We have two main contributions. The first is the design of adjustable FIR filters without discretization, using 2D positive trigonometric polynomials, an approach leading to semidefinite programming (SDP) formulation of the design problem. The second is to modify the design problem by a special choice for the passband and stopband edges of the variable FIR filter. The advantage is a lower implementation complexity. The new problem is solved using positive hybrid real-trigonometric polynomials and their SDP parameterization. Design examples prove the viability of our methods.
A large number of interesting combinatorial optimization problems like MAX CUT, MAX k-SAT, and UNIQUE GAMES fall under the class of constraint satisfaction problems (CSPs). Recent work [32] by one of the authors ident...
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ISBN:
(纸本)9780769538501
A large number of interesting combinatorial optimization problems like MAX CUT, MAX k-SAT, and UNIQUE GAMES fall under the class of constraint satisfaction problems (CSPs). Recent work [32] by one of the authors identifies a semidefinite programming (SDP) relaxation that yields the optimal approximation ratio for every CSP, under the Unique Games Conjecture (UGC). Very recently [33], the authors also showed unconditionally that the integrality gap of this basic SDP relaxation cannot be reduced by adding large classes of valid inequalities (e.g., in the fashion of Sherali-Adams LP hierarchies). In this work, we present an efficient rounding scheme that achieves the integrality gap of this basic SDP relaxation for every CSP (and by [33] it also achieves the gap of much stronger SDP relaxations). The SDP relaxation we consider is stronger or equivalent to any relaxation used in literature to approximate CSPs. Thus, irrespective of the truth of the UGC, our work yields an efficient generic algorithm that for every CSP, achieves an approximation at least as good as the best known algorithm in literature. The rounding algorithm in this paper can be summarized succinctly as follows: Reduce the dimension of SDP solution by random projection, discretize the projected vectors, and solve the resulting CSP instance by brute force! Even the proof is simple in that it avoids the use of the machinery from unique games reductions such as dictatorship tests, Fourier analysis or the invariance principle. A common theme of this paper and the subsequent paper [33] is a robustness lemma for SDP relaxations which asserts that approximately feasible solutions can be made feasible by "smoothing" without changing the objective value significantly.
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