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Robust secure transmission for multiuser MISO systems with probabilistic QoS constraints

Science China(Information Sciences) 2016年第2期59卷 126-138页

作者： Lijian ZHANG Liang JIN Wenyu LUO Chunming WANG Yanqun TANG National Digital Switching System Engineering & Technological Research Center School of Information Systems Engineering Zhengzhou Information Science and Technology Institute

This paper considers a unicast multiuser multiple-input single-output(MISO) downlink system overheard by multiple single-antenna eavesdroppers. The objective is to jointly design the beamforming vectors and the artificial noise(AN) covariance matrix with imperfect channel state information(CSI) at the transmitter,such that the total transmit power is minimized while satisfying probabilistic quality of service(Qo S) constraints at legitimate users and the eavesdroppers. Using Bernstein-type inequalities and the S-procedure, we recast the non-convex power minimization problem as two different convex semidefinite programs(SDPs) which can be solved using interior-point methods. Simulation results show that the proposed methods outperform a nonrobust method and the ones using the isotropic AN.

关键词： physical layer security artificial noise imperfect CSI robust beamforming semidefinite program outage probability

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A Hybrid Transmission Grid Architecture Enabling Efficient Optimal Power Flow

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IEEE TRANSACTIONS ON POWER SYSTEMS 2016年第6期31卷 4504-4516页

作者： Hotz, Matthias Utschick, Wolfgang Tech Univ Munich Dept Elect & Comp Engn D-80333 Munich Germany

The recent rise of electricity generation based on renewable energy sources increases the demand for transmission capacity. Capacity expansion via the upgrade of transmission line capacity, e.g., by conversion to a high-voltage direct current (HVDC) line, is an attractive option. In this paper, it is shown that if the upgrade to HVDC is applied systematically to selected transmission lines across the grid, a hybrid architecture is obtained that enables an efficient and globally optimal solution of the optimal power flow (OPF) problem. More precisely, for conventional meshed AC transmission grids the OPF problem is nonconvex and in general NP-hard, rendering it hard to solve. We prove that after the upgrade to the proposed hybrid architecture, the same mesh topology facilitates an exact convex relaxation of the OPF problem, enabling its globally optimal solution with efficient polynomial time algorithms. This OPF method is then employed in simulations, which demonstrate that the hybrid architecture can increase the effective transmission capacity and substantially reduce the generation costs, even compared to the AC grid with optimal transmission switching.

关键词： Congestion management convex relaxation economic dispatch HVDC transmission optimal power flow optimal transmission switching power system design power system management semidefinite program transmission capacity

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Promises of Conic Relaxation for Contingency-Constrained Optimal Power Flow Problem

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IEEE TRANSACTIONS ON POWER SYSTEMS 2016年第2期31卷 1297-1307页

作者： Madani, Ramtin Ashraphijuo, Morteza Lavaei, Javad Columbia Univ Dept Elect Engn New York NY 10027 USA

This paper is concerned with the security-constrained optimal power flow (SCOPF) problem, where each contingency corresponds to the outage of an arbitrary number of lines and generators. The problem is studied by means of a convex relaxation, named semidefinite program (SDP). The existence of a rank-1 SDP solution guarantees the recovery of a global solution of SCOPF. We prove that the rank of the SDP solution is upper bounded by the treewidth of the power network plus one, which is perceived to be small in practice. We then propose a decomposition method to reduce the computational complexity of the relaxation. In the case where the relaxation is not exact, we develop a graph-theoretic convex program to identify the problematic lines of the network and incorporate the loss over those lines into the objective as a penalization (regularization) term, leading to a penalized SDP problem. We perform several simulations on large-scale benchmark systems and verify that the global minima are at most 1% away from the feasible solutions obtained from the proposed penalized relaxation.

关键词： Convex relaxation graph theory optimal power flow security-constrained optimal power flow semidefinite program

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Robust Optimization of Sums of Piecewise Linear Functions with Application to Inventory Problems

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OPERATIONS RESEARCH 2016年第2期64卷 474-494页

作者： Ardestani-Jaafari, Amir Delage, Erick HEC Montreal Dept Decis Sci Montreal PQ H3T 2A7 Canada

Robust optimization is a methodology that has gained a lot of attention in the recent years. This is mainly due to the simplicity of the modeling process and ease of resolution even for large scale models. Unfortunately, the second property is usually lost when the cost function that needs to be "robustified" is not concave (or linear) with respect to the perturbing parameters. In this paper we study robust optimization of sums of piecewise linear functions over polyhedral uncertainty set. Given that these problems are known to be intractable, we propose a new scheme for constructing conservative approximations based on the relaxation of an embedded mixed-integer linear program and relate this scheme to methods that are based on exploiting affine decision rules. Our new scheme gives rise to two tractable models that, respectively, take the shape of a linear program and a semidefinite program, with the latter having the potential to provide solutions of better quality than the former at the price of heavier computations. We present conditions under which our approximation models are exact. In particular, we are able to propose the first exact reformulations for a robust (and distributionally robust) multi-item newsvendor problem with budgeted uncertainty set and a reformulation for robust multiperiod inventory problems that is exact whether the uncertainty region reduces to a L-1-norm ball or to a box. An extensive set of empirical results will illustrate the quality of the approximate solutions that are obtained using these two models on randomly generated instances of the latter problem.

关键词： optimization piecewise linear linear programming relaxation semidefinite program tractable approximations newsvendor problem inventory problem

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Robust Localization Using Time Difference of Arrivals

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IEEE SIGNAL PROCESSING LETTERS 2016年第10期23卷 1320-1324页

作者： Shi, Xiufang Anderson, Brian. D. O. Mao, Guoqiang Yang, Zaiyue Chen, Jiming Lin, Zihuai Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Australian Natl Univ Res Sch Engn Canberra ACT 0200 Australia Data61 CSIRO Canberra ACT 2601 Australia Univ Technol Sydney Sch Comp & Commun Sydney NSW 2007 Australia Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

We investigate a localization problem using time-difference-of-arrival measurements with unknown and bounded measurement errors. Different from most existing algorithms, we consider the minimization of the worst-case position estimation error to improve the robustness of the algorithm. The localization problem is formulated as a nonconvex optimization problem. We adopt semidefinite relaxation to relax the original problem into a convex optimization problem, which can be solved using existing semidefinite program solvers. Simulation results show that our proposed algorithm has lower worst-case position estimation error than other existing algorithms.

关键词： Chebyshev center semidefinite program time difference of arrival worst-case estimation error

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EEG channel optimization via sparse common spatial filter

EEG channel optimization via sparse common spatial filter

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Quan Zhou Aimin Jiang Xiaofeng Liu College of Internet of Things Engineering Hohai University Changzhou China

ISBN: (纸本)9781509041183

In this paper, we propose a novel sparse common spatial pattern (CSP) algorithm to optimally select channels of EEG signals. Compared to the traditional CSP, which maximizes the variance of signals in one class and minimizes the variance of signals in the other class, the classification accuracy is guaranteed by a constraint that the ratio of variances of signals in two different classes is lower bounded. Then, a sparse spatial filter is achieved by minimizing the l1-norm of filter coefficients and channels of EEG signals can be further optimized. The original nonconvex optimization problem is relaxed to a semidefinite program (SDP), which can be efficiently solved by well-developed numerical solvers. Experimental results demonstrate that the proposed algorithm can identify and discard about 50% channels with only 1% decrease of classification accuracy.

关键词： Channel optimization common spatial pattern (CSP) EEG semidefinite program sparsity Electroencephalography signals Spatial filters Filter coefficient Variance communicating sequential processes chip scale packaging phosphocellulose

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A Novel SDP Relaxation for the Quadratic Assignment Problem Using Cut Pseudo Bases 4th

A Novel SDP Relaxation for the Quadratic Assignment Problem ...

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4th International Symposium on Combinatorial Optimization (ISCO)

作者： John, Maximilian Karrenbauer, Andreas Max Planck Inst Informat Saarbrucken Germany

ISBN: (纸本)9783319455877;9783319455860

The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems. Its range of applications is wide, including facility location, keyboard layout, and various other domains. The key success factor of specialized branch-and-bound frameworks for minimizing QAPs is an efficient implementation of a strong lower bound. In this paper, we propose a lower-bound-preserving transformation of a QAP to a different quadratic problem that allows for small and efficiently solvable SDP relaxations. This transformation is self-tightening in a branch-and-bound process.

关键词： Quadratic assignment semidefinite program Lower bound Branch and bound

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The matrix mechanism: optimizing linear counting queries under differential privacy

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VLDB JOURNAL 2015年第6期24卷 757-781页

作者： Li, Chao Miklau, Gerome Hay, Michael McGregor, Andrew Rastogi, Vibhor Univ Massachusetts Coll Informat & Comp Sci Amherst MA 01003 USA Colgate Univ Dept Comp Sci Hamilton NY USA Twitter Inc San Francisco CA USA

Differential privacy is a robust privacy standard that has been successfully applied to a range of data analysis tasks. We describe the matrix mechanism, an algorithm for answering a workload of linear counting queries that adapts the noise distribution to properties of the provided queries. Given a workload, the mechanism uses a different set of queries, called a query strategy, which are answered using a standard Laplace or Gaussian mechanism. Noisy answers to the workload queries are then derived from the noisy answers to the strategy queries. This two-stage process can result in a more complex, correlated noise distribution that preserves differential privacy but increases accuracy. We provide a formal analysis of the error of query answers produced by the mechanism and investigate the problem of computing the optimal query strategy in support of a given workload. We show that this problem can be formulated as a rank-constrained semidefinite program. We analyze two seemingly distinct techniques proposed in the literature, whose similar behavior is explained by viewing them as instances of the matrix mechanism. We also describe an extension of the mechanism in which nonnegativity constraints are included in the derivation process and provide experimental evidence of its efficacy.

关键词： Differential privacy Linear query Matrix mechanism semidefinite program Least squares

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Robust Transceiver Optimization for Power-Splitting Based Downlink MISO SWIPT Systems

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IEEE SIGNAL PROCESSING LETTERS 2015年第9期22卷 1492-1496页

作者： Wang, Feng Peng, Tao Huang, Yongwei Wang, Xin Fudan Univ Key Lab Informat Sci Electromagnet Waves MoE Shanghai 200433 Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Hong Kong Peoples R China

This letter considers a downlink multi-input single-out (MISO) system where each user performs simultaneous wireless information and power transfer (SWIPT) based on a power splitting receiver architecture. Assuming imperfect channel state information (CSI) at the base station, we develop two robust joint beamforming and power splitting (BFPS) designs that minimize the transmission power under both the signal-to-interference-plus-noise ratio (SINR) and energy harvesting (EH) constraints per user. In the first design, we consider the worst-case (WC) SINR and EH constraints, and show that the WC-BFPS problem can be relaxed as a semidefinite program (SDP) through a linear matrix inequality representation for (infinitely many) robust quadratic matrix inequality constraints. In the second design, we consider the chance constraints (CCs) for SINR and EH, and resort to both semidefinite relaxation and Bernstein-type inequality restriction to transform the CC-BFPS problem into another convex SDP. Based on these convex reformulations, the (near-) optimal robust BFPS designs can be efficiently solved. Numerical results are provided to demonstrate the merit of the proposed robust designs.

关键词： Bernstein-type inequality energy harvesting power splitting robust beamforming semidefinite program

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Robust beamforming designs for multiuser MISO downlink with per-antenna power constraints

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2015年第1期2015卷 1-16页

作者： Wang, Feng Huang, Yongwei Wang, Xin Zhu, Yu Fudan Univ Key Lab Informat Sci Electromagnet Waves MoE Dept Commun Sci & Engn 220 Han Dan Rd Shanghai Peoples R China Hong Kong Baptist Univ Dept Math Hong Kong Hong Kong Peoples R China

This paper studies the robust beamforming designs for a multiuser multiple-input single-output (MISO) downlink system. Different from the conventional sum-power constraint across all transmit antennas, we consider individual power constraints per antenna at the base station. Assuming that the channel uncertainty is bounded by a spherical region, we develop the optimal robust designs to maximize the minimum worst-case signal-to-interference-plus-noise ratio (SINR) among all users. Specifically, we show that the optimal max-min SINR beamformers can be obtained by solving a sequence of "dual" min-max power problems. Relying on the S-procedure and the linear matrix inequality representation for the cone of Lorentz-positive maps (LPMs), respectively, two designs, which are referred to as Robust-SP and Robust-LPM, are proposed to efficiently solve such min-max power problems. Building on either Robust-SP or Robust LPM, a bisection search algorithm is then developed to find the robust max-min SINR beamformers with guaranteed global optimality and geometrically fast convergence speed. Using the max-min SINR solutions as a cornerstone, we further put forth the optimal robust design for the worst-case weighted sum-rate (WSR) maximization. By formulating the worst-case WSR maximization problem into a monotonic program (MP), we develop a polyblock outer approximation algorithm to obtain the globally optimal solution. Numerical results are presented to demonstrate the merits of the proposed robust beamforming designs.

关键词： Lorentz-positive maps MISO robust beamforming Monotonic program Per-antenna power constraints semidefinite program

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