In this paper, we propose a two stage stochastic binary quadratic program for OFDMA wireless networks. The aim is to minimize the total power consumption of the network subject to user bit rates, sub-carrier and modul...
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We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interi...
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ISBN:
(纸本)9780898715859
We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in R-2 using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable sub-networks in the input network.
In a previous work, a universal decoder in a competitive minimax sense was developed for unknown block fading linear white Gaussian channels. For a given codebook (with finite blocklength), a high SNR optimal metric f...
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ISBN:
(纸本)9781457705953
In a previous work, a universal decoder in a competitive minimax sense was developed for unknown block fading linear white Gaussian channels. For a given codebook (with finite blocklength), a high SNR optimal metric for the decoder was found, whose direct calculation requires solving a non-convex optimization problem and may be formidable. In this paper, the metric calculation problem is facilitated by semidefinite programming, which leads to a low-complexity approximation for the metric. The competitive minimax performance of the optimal decoder (i.e., its worst case power loss compared to the maximum likelihood decoder, which has full knowledge of the channel) is evaluated, and upper lower bounds are derived for the performance evaluation of non-optimal decoders - the training sequence and the generalized likelihood test decoders.
Many hierarchies of lift-and-project relaxations for 0,1 integer programs have been proposed, two of the most recent and strongest being those by Lasserre in 2001, and Bienstock and Zuckerberg in 2004. We prove that, ...
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ISBN:
(纸本)9783642208072
Many hierarchies of lift-and-project relaxations for 0,1 integer programs have been proposed, two of the most recent and strongest being those by Lasserre in 2001, and Bienstock and Zuckerberg in 2004. We prove that, on the LP relaxation of the matching polytope of the complete graph on (2n+1) vertices defined by the nonnegativity and degree constraints, the Bienstock-Zuckerberg operator (even with positive semidefiniteness constraints) requires Theta(root n) rounds to reach the integral polytope, while the Lasserre operator requires Theta(n) rounds. We also prove that Bienstock-Zuckerberg operator, without the positive semidefiniteness constraint requires approximately n/2 rounds to reach the stable set polytope of the n-clique, if we start with the fractional stable set polytope. As a by-product of our work, we consider a significantly strengthened version of Sherali-Adams operator and a strengthened version of Bienstock-Zuckerberg operator. Most of our results also apply to these stronger operators.
A new exact approach to the stable set problem is presented, which attempts to avoids the pitfalls of existing approaches based on linear and semidefinite programming. The method begins by constructing an ellipsoid th...
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ISBN:
(纸本)9783642208072
A new exact approach to the stable set problem is presented, which attempts to avoids the pitfalls of existing approaches based on linear and semidefinite programming. The method begins by constructing an ellipsoid that contains the stable set polytope and has the property that the upper bound obtained by optimising over it is equal to the Lovasz theta number. This ellipsoid is then used to derive cutting planes, which can be used within a linear programming-based branch-and-cut algorithm. Preliminary computational results indicate that the cutting planes are strong and easy to generate.
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definit...
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We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of departure functions. We use these characterizations to construct effective algorithms for approximating a single correlated equilibrium or the entire set of correlated equilibria of a game with polynomial utility functions. (C) 2010 Elsevier Inc. All rights reserved.
One of the beautiful results due to Grötschel, Lovász and Schrijver is the fact that the theta body of a graph G is polyhedral if and only if G is perfect. Related to the theta body of G is a foundational co...
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We give the first tight integrality gap for Vertex Cover in the Sherali-Adams SDP system. More precisely, we show that for every c > 0, the standard SDP for Vertex Cover that is strengthened with the level-6 Sheral...
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ISBN:
(纸本)9783939897347
We give the first tight integrality gap for Vertex Cover in the Sherali-Adams SDP system. More precisely, we show that for every c > 0, the standard SDP for Vertex Cover that is strengthened with the level-6 Sherali-Adams system has integrality gap 2 - c. To the best of our knowledge this is the first nontrivial tight integrality gap for the Sherali-Adams SDP hierarchy for a combinatorial problem with hard constraints. For our proof we introduce a new tool to establish Local-Global Discrepancy which uses simple facts from high-dimensional geometry. This allows us to give Sherali-Adams solutions with objective value n(1/2 + o(1)) for graphs with small (2 + o(1)) vector chromatic number. Since such graphs with no linear size independent sets exist, this immediately gives a tight integrality gap for the Sherali-Adams system for superconstant number of tightenings. In order to obtain a Sherali-Adams solution that also satisfies semidefinite conditions, we reduce semidefiniteness to a condition on the Taylor expansion of a reasonably simple function that we are able to establish up to constant-level SDP tightenings. We conjecture that this condition holds even for superconstant levels which would imply that in fact our solution is valid for superconstant level Sherali-Adams SDPs.
This paper deals with the generalization of the theorems of alternatives in semidefinite programming proposed by Balakrishnan and Vandenberghe. In their original form, the theorems assume that the domain of the linear...
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ISBN:
(纸本)9781424415304
This paper deals with the generalization of the theorems of alternatives in semidefinite programming proposed by Balakrishnan and Vandenberghe. In their original form, the theorems assume that the domain of the linear mapping be a finite-dimensional Hilbert space. We show that the validity of the basic theorems does not rely on the finite-dimensional assumption, and the derived theorems can also be appropriately generalized. The Moore-Penrose inverse plays a crucial role in the generalization.
In this paper, we design downlink (DL) beamforming vectors for a multiuser multicell network when only imperfect knowledge of the channel covariance is available at base stations. Specifically, we consider two differe...
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ISBN:
(纸本)9781424492688
In this paper, we design downlink (DL) beamforming vectors for a multiuser multicell network when only imperfect knowledge of the channel covariance is available at base stations. Specifically, we consider two different models for covariance errors: a) deterministic error bounded in a spherical region and b) stochastic error with known probability distribution. Our objective is to minimize the total DL transmit power subject to quality of service (QoS) constraint of every user. It is shown that for both uncertainty models, the optimization can be formulated as a convex semidefinite programming (SDP) problem using the standard rank relaxation approach. Interestingly, numerical results show that the obtained solutions fulfill the rank constraint and are therefore exact.
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