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LINEARLY CONVERGENT FIRST-ORDER ALGORITHMS FOR semidefinite programming

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Journal of Computational Mathematics 2017年第4期35卷 452-468页

作者： Cong D. Dang Guanghui Lan Zaiwen Wen Department of Industrial and Systems Engineering University of Florida Gainesville FL 32611 H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of TechnologyAtlanta GA 30332 USA Beijing International Center for Mathematical Research Peking University Beijing 100871 China

In this paper, we consider two different formulations （one is smooth and the other one is nonsmooth） for solving linear matrix inequalities （LMIs）, an important class of semidefinite programming （SDP）, under a certain Slater constraint qualification assumption. We then propose two first-order methods, one based on subgradient method and the other based on Nesterov＇s optimal method, and show that they converge linearly for solving these formulations. Moreover, we introduce an accelerated prox-level method which converges linearly uniformly for both smooth and non-smooth problems without requiring the input of any problem parameters. Finally, we consider a special case of LMIs, i.e., linear system of inequalities, and show that a linearly convergent algorithm can be obtained under a much weaker assumption.

关键词： semi-definite programming Linear Matrix Inequalities Error Bounds Linear Convergence

FIRST-ORDER METHODS FOR SOLVING THE OPTIMAL STATIC H∞-SYNTHESIS PROBLEM

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Journal of Computational Mathematics 2007年第6期25卷 672-689页

作者： El-Sayed M.E. Mostafa Department of Mathematics Faculty of Science Alexandria University Alexandria Egypt

In this paper, we consider the static output feedback （SOF） H∞-synthesis problem posed as a nonlinear semi-definite programming （NSDP） problem. Two numerical algorithms are developed to tackle the NSDP problem by solving the corresponding Karush- Kuhn-Tucker first-order necessary optimality conditions iteratively. Numerical results for various benchmark problems illustrating the performance of the proposed methods are given.

关键词： Static output feedback H∞-synthesis semi-definite programming Nonlinear programming.

NEW ROBUST UNSUPERVISED SUPPORT VECTOR MACHINES

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Journal of Systems Science & Complexity 2011年第3期24卷 466-476页

作者： Kun ZHAO Mingyu ZHANG ~ Naiyang DENG Logistics School Beijing Wuzi University Beijing 101149 China. School of Economic and Management Beijing Jiaotong University Beijing 100044 China. College of Science China Agricultural University Bcijing 100083 China.

This paper proposes robust version to unsupervised classification algorithm based on modified robust version of primal problem of standard SVMs, which directly relaxes it with label variables to a semi-definite progra... 详细信息

关键词： Robust semi-definite programming support vector machines unsupervised learning

semi-definite RELAXATION ALGORITHM FOR SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES

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Chinese Annals of Mathematics,Series B 2005年第1期26卷 153-158页

作者： CHENFENG ZHANGLIANSHENG DepartmentofMathematics ShanghaiUniversityShanghai200436China／／DepartmentofIndustrialEngineeringandManagementShanghaiJiaotongUniversityShanghai200030China. DepartmentofMathematics ShanghaiUniversityShanghai200436China

The authors present a semi-definite relaxation algorithm for the scheduling problem with controllable times on a single machine. Their approach shows how to relate this problem with the maximum vertex-cover problem with kernel constraints (MKVC).The established relationship enables to transfer the approximate solutions of MKVCinto the approximate solutions for the scheduling problem. Then, they show how to obtain an integer approximate solution for MKVC based on the semi-definite relaxation and randomized rounding technique.

关键词： Scheduling with controllable times semi-definite programming Approximation algorithm

Integrating outlier filtering in large margin training

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Journal of Zhejiang University-Science C(Computers and Electronics) 2011年第5期12卷 362-370页

作者： Xi-chuan ZHOU Hai-bin SHEN Jie-ping YE College of Communication Engineering Chongqing University Chongqing 400044 China School of Electrical Engineering Zhejiang University Hangzhou 310027 China Dcpartment of Computer Science and Engineering Arizona State University Tempe 85281 USA

Large margin classifiers such as support vector machines (SVM) have been applied successfully in various classification ***,their performance may be significantly degraded in the presence of *** this paper,we propose a robust SVM formulation which is shown to be less sensitive to *** key idea is to employ an adaptively weighted hinge loss that explicitly incorporates outlier filtering in the SVM training,thus performing outlier filtering and classification *** resulting robust SVM formulation is *** first relax it into a semi-definite programming which admits a global *** improve the efficiency,an iterative approach is *** have performed experiments using both synthetic and real-world *** show that the performance of the standard SVM degrades rapidly when more outliers are included,while the proposed robust SVM training is more stable in the presence of outliers.

关键词： Support vector machines Outlier filter semi-definite programming Multi-stage relaxation

Robust MIMO Precoding for Cognitive Multiuser Relay Networks with Imperfect Channel State Information

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Transactions of Tianjin University 2016年第6期22卷 590-595页

作者：俎云霄揭昕政 School of Electronic Engineering Beijing University of Posts and Telecommunications Beijing 100876 China

In this paper, a novel robust precoder with imperfect channel state information(CSI)is proposed for multi-input multi-output(MIMO)cognitive multiuser networks equipped with relays. In the proposed model, the secondary users(SUs)are allowed to share the spectrum with the primary users(PUs)when the interference temperature(IT)is below a specific threshold. The transmitting strategy of relays is amplify-and-forward(AF), and the CSI error is characterized in terms of spherical uncertainty region. A minmax problem for the transmit power of the relays is considered when the mean square error(MSE)of SUs and the IT of PU meet their corresponding thresholds, and it is transformed into a semi-definite programming(SDP)problem to search for the solution. Numerical simulations demonstrate the effectiveness of the proposed precoder.

关键词： cognitive radio multi-input multi-output imperfect channel state information semi-definite programming robust precoding

Performance analysis of ultra-wideband based wireless sensor networks in indoor office LOS environment

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Journal of Harbin Institute of Technology(New Series) 2012年第5期19卷 101-106页

作者：吴宣利罗超杨孝宗孙陆宽曹阳 School of Computer Science and Technology Harbin Institute of Technology School of Electronics and Information Engineering Harbin Institute of Technology

By analyzing the indoor office LOS channel model defined by IEEE 802.15.4a standard and deducing the variance for intra-symbol interference (IASI), inter-symbol interference (ISI) and multiuser interference (MUI), performance analysis model for ultra-wideband (UWB) based wireless sensor networks (WSN) is proposed, and the bit error rate (BER) formulation is also obtained. The comparison of performance analysis model with and without intra-symbol interference shows that the intra-symbol interference cannot be neglected and such interference will significantly decrease the system performance. In order to verify the proposed performance analysis model and BER formulation, the semi-definite programming (SDP) algorithm is used to obtain the pulses complying with the spectrum requirement of China and IEEE 802.15.4a standard, and by using such pulses, simulations and theoretical analysis are compared, the comparison results show the validity of the proposed performance analysis model and BER formulation.

关键词： ultra-wideband IEEE 802.15.4a BER performance analysis semi-definite programming

Optimal Energy Consensus Control for Linear Multi-Agent Systems

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Optimal Energy Consensus Control for Linear Multi-Agent Syst...

Wireless Sensor Network Localization Using SDP Relaxation

第36届中国控制会议

作者： Han Zhang Xiaoming Hu Department of Mathematics KTH Royal Institute of Technology

ISBN: (纸本)9781538629185

In this paper, an optimal energy cost controller for linear multi-agent systems’ consensus is proposed. It is assumed that the topology among the agents is fixed and the agents are connected through an edge-weighted graph. The controller only uses relative information between agents. Due to the difficulty of finding the controller gain, we focus on finding the optimal controller among a sub-family whose design is based on Algebraic Riccati Equation（ARE） and guarantee consensus. It is found that the energy cost for such controllers is bounded by an interval and hence we minimize the upper bound. To do that, the control gain and the edge weights are optimized separately. The control gain is optimized by choosing Q = 0 in the ARE;the edge weights are optimized under the assumption that there is limited communication resources in the network. Negative edge weights are allowed, and the problem is formulated as a semi-definite programming（SDP） problem. The controller coincides with the optimal control in [8] when the graph is complete. Furthermore, two sufficient conditions for the existence of negative optimal edge weights realization are given.

关键词： Consensus Control Multi-Agent Systems Optimal Control semi-definite programming Synchronizability

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Wireless Sensor Network Localization Using SDP Relaxation