We study disjunctive conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone, or the positive semidefinite cone. In a unified fra...
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We study disjunctive conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone, or the positive semidefinite cone. In a unified framework, we introduce K-minimal inequalities and show that, under mild assumptions, these inequalities together with the trivial cone-implied inequalities are sufficient to describe the convex hull. We focus on the properties of K-minimal inequalities by establishing algebraic necessary conditions for an inequality to be K-minimal. This characterization leads to a broader algebraically defined class of K-sublinear inequalities. We demonstrate a close connection between K-sublinear inequalities and the support functions of convex sets with a particular structure. This connection results in practical ways of verifying K-sublinearity and/or K-minimality of inequalities. Our study generalizes some of the results from the mixedinteger linear case. It is well known that the minimal inequalities for mixedinteger linear programs are generated by sublinear (positively homogeneous, subadditive, and convex) functions that are also piecewise linear. Our analysis easily recovers this result. However, in the case of general regular cones other than the nonnegative orthant, our study reveals that such a cut-generating function view, which treats the data associated with each individual variable independently, is far from sufficient.
Coordinated Multi-Point Transmission (CoMP) has been proposed for 4G standards, like WiMAX and LTE-Advanced, as an effective mean to control intercell interference and to increase spectral efficiency in single frequen...
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ISBN:
(纸本)9781467300469
Coordinated Multi-Point Transmission (CoMP) has been proposed for 4G standards, like WiMAX and LTE-Advanced, as an effective mean to control intercell interference and to increase spectral efficiency in single frequency reuse networks. In practical systems, the remarkable benefits of CoMP operation over conventional single basestation transmission need to be traded against a significant overhead in network complexity and associated operational costs. In order to retain the benefits of CoMP at reasonable costs, we consider the problem of joint basestation selection and multicell beamforming (JBSB). We address this problem via a mixedinteger second order cone programming (MI-SOCP) approach. We propose a novel MI-SOCP formulation of the JBSB problem and a reformulation with tighter continuous relaxations. Based on this formulation, we propose fast algorithms to find almost optimal feasible solutions. We show via simulations that the proposed algorithms outperform existing solutions in terms of both complexity and total transmitted power at a guaranteed signal-to-interference-plus-noise-ratio (SINR) level at each mobile station (MS).
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