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Journal of Modern Power Systems and Clean Energy 2022年第6期10卷 1614-1624页

作者： Yanling Lin Xiaohu Zhang Jianhui Wang Di Shi Desong Bian GEIRI North America San JoseUSA Southern Methodist University DallasUSA

This paper proposes a voltage stability constrained optimal power flow(VSC-OPF)for an unbalanced distribution system with distributed generators(DGs)based on semidefinite programming(SDP).The AC optimal power flow(ACOPF)for unbalanced distribution systems is formulated as a chordal relaxation-based SDP model.The minimal singular value(MSV)of the power flow Jacobian matrix is adopted to indicate the voltage stability margin.The Jacobian matrix can be explicitly expressed by ACOPF state variables.The nonlinear constraint on the Jacobian MSV is then replaced with its maximal convex subset using linear matrix inequality(LMI),which can be incorporated in the SDP-based ACOPF formulation.A penalty technique is leveraged to improve the exactness of the SDP relaxation.Case studies performed on several IEEE test systems validate the effectiveness of the proposed method.

关键词： Voltage stability semidefinite programming Jacobian matrix optimal power flow

semidefinite programming detection for OvHDM signal

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The Journal of China Universities of Posts and Telecommunications 2008年第3期15卷 8-12,18页

作者： MO Yong YANG Xing LI Dao-ben School of Information Engineering Beijing University of Posts and Telecommunications Beijing 100876 China

Non-orthogonal time-frequency division multiplexing （NTFDM） transmission scheme has been proposed to further improve the bandwidth efficiency and overcome the drawbacks of the conventional orthogonal frequency division multiplexing （OFDM） method. Based on such approach, the fast signal detection algorithm, semidefinite programming （SDP） detection, has been studied. As the coefficient matrix tends to be ill conditioned, the modified SDP algorithm combined with successive interference cancellation （SIC） has been developed. The improved algorithm is a good tradeoff between performance and detection complexity. Simulation results show that the proposed algorithm can achieve better performance than cutting plane aided SDP method.

关键词： overlapped TDM （OvTDM） overlapped frequency division multiplexing （OvFDM） overlapped hybrid division multiplexing （OvHDM） semidefinite programming successive interference cancellation

Incorporating Convexity in Bond Portfolio Immunization Using Multifactor Model:A semidefinite programming Approach

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Journal of the Operations Research Society of China 2018年第1期6卷 3-23页

作者： Wei Zhu Cai-Hong Zhang Qian Liu Shu-Shang Zhu Department of Finance and Investment Sun Yat-Sen Business SchoolSun Yat-Sen UniversityGuangzhou 510275China Ping An Securities Company Ltd Beijing 100033China

Bond portfolio immunization is a classical issue in finance. Since Macaulaygave the concept of duration in 1938, many scholars proposed different kinds of duration immunization models. In the literature of bond portfolio immunization usingmultifactor model, to the best of our knowledge, researchers only use the first-orderimmunization, which is usually called as duration immunization, and no one hasconsidered second-order effects in immunization, which is well known as “convexity” in the case of single-factor model. In this paper, we introduce the second-orderinformation associated with multifactor model into bond portfolio immunization andreformulate the corresponding problems as tractable semidefinite programs. Bothsimulation analysis and empirical study show that the second-order immunization strategies exhibit more accurate approximation to the value change of bonds and thusresult in better immunization performance.

关键词： Immunization Duration Convexity Multifactor model semidefinite programming

UV -theory of a Class of semidefinite programming and Its Applications

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Acta Mathematicae Applicatae Sinica 2021年第4期37卷 717-737页

作者： Ming HUANG Jin-long YUAN Li-ping PANG Zun-quan XIA School of Science Dalian Maritime UniversityDalian116026China School of Mathematical Science Dalian University of TechnologyDalian116023China

In this paper we study optimization problems involving convex nonlinear semidefinite programming(CSDP).Here we convert CSDP into eigenvalue problem by exact penalty function,and apply the U-Lagrangian theory to the function of the largest eigenvalues,with matrix-convex valued mappings.We give the first-and second-order derivatives of U-Lagrangian in the space of decision variables Rm when transversality condition holds.Moreover,an algorithm frame with superlinear convergence is presented.Finally,we give one application:bilinear matrix inequality(BMI)optimization;meanwhile,list their UV decomposition results.

关键词： semidefinite programming nonsmooth optimization eigenvalue optimization UV-decomposition,u-Lagrangian smooth manifold second-order derivative

ON DOUBLY POSITIVE semidefinite programming RELAXATIONS

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Journal of Computational Mathematics 2018年第3期36卷 391-403页

作者： Taoran Fu Dongdong Ge Yinyu Ye School of Mathematical Sciences Shanghai Jiao Tong University Shanghai China School of Information Management and Engineering Shanghai University of Finance and Economics Shanghai 200433 China Department of Management Science and Engineering Stanford University Stanford CA 94305

Recently, researchers have been interested in studying the semidefinite programming （SDP） relaxation model, where the matrix is both positive semidefinite and entry-wise nonnegative, for quadratically constrained quadratic programming （QCQP）. Comparing to the basic SDP relaxation, this doubly-positive SDP model possesses additional O（n2） constraints, which makes the SDP solution complexity substantially higher than that for the basic model with O（n） constraints. In this paper, we prove that the doubly-positive SDP model is equivalent to the basic one with a set of valid quadratic cuts. When QCQP is symmetric and homogeneous （which represents many classical combinatorial and non- convex optimization problems）, the doubly-positive SDP model is equivalent to the basic SDP even without any valid cut. On the other hand, the doubly-positive SDP model could help to tighten the bound up to 36%, but no more. Finally, we manage to extend some of the previous results to quartic models.

关键词： Doubly nonnegative matrix semidefinite programming Relaxation Quarticoptimization

Minimum-Error Quantum State Discrimination Based on semidefinite programming

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Minimum-Error Quantum State Discrimination Based on Semidefi...

A Proof of the Discrete-Time KYP Lemma Using semidefinite programming Duality

第二十七届中国控制会议

作者： Wang Wengang,Dong Guohua,Li Mingshan Department of Automatic Control,National University of Defense Technology,Changsha 410073,P.R.China

In this paper we consider the general problem of designing the optimal quantum detection for minimum-error quantum state discrimination.Since it is hard to get an explicit solution and we must resort to numerical methods for the general case.We show the problem can be cast into a semidefinite programming(SDP) problem,we use the theory of SDP to solve it.Based on the idea,we propose a method for minimum-error discrimination by formulating the design of optimal quantum detection as a standard SDP problem;furthermore,based on the optimality conditions for SDP,we derive a set of optimality conditions for quantum detection.It is exemplified that this method is simple to implement and can be used to design optimum detection operators for minimum-error discrimination efficiently.

关键词： semidefinite programming Quantum states Minimum-error discrimination

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A Proof of the Discrete-Time KYP Lemma Using Semidefinite Pr...

Beamforming design for RIS-aided amplify-and-forward relay networks

第二十六届中国控制会议

作者： Cheng Yiping School of Electronic and Information Engineering Beijing Jiaotong University,Beijing 100044,P.R.China

Balakrishnan and Vandenberghe have given an elegant proof of the KYP lemma based on their theorems of alternatives in semidefinite programming.Based also on these theorems,this paper gives a proof of a generalized version of the discrete-time KYP lemma.In addition,we point out that in the nonstrict case of Balakrishnan and Vandenberghe’s （continuous-time） KYP formulation the hypothesis that M22 be positive semidefinite can be dropped.

关键词： Discrete-time KYP lemma Linear matrix inequalities semidefinite programming Control education

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Frontiers of Information Technology & Electronic Engineering 2023年第12期24卷 1728-1738页

作者： Xuehui WANG Feng SHU Riqing CHEN Peng ZHANG Qi ZHANG Guiyang XIA Weiping SHI Jiangzhou WANG School of Information and Communication Engineering Hainan UniversityHaikou570228China School of Electronic and Optical Engineering Nanjing University of Science and TechnologyNanjing210094China Digital Fujian Institute of Big Data for Agriculture Fujian Agriculture and Forestry UniversityFuzhou350002China Institute of Intelligent Agriculture Anhui Agricultural UniversityHefei230036China School of Engineering University of KentCanterburyCT27NTUK

The use of a reconfigurable intelligent surface(RIS)in the enhancement of the rate performance is considered to involve the limitation of the RIS being a passive reflector.To address this issue,we propose a RIS-aided amplify-and-forward(AF)relay network in this paper.By jointly optimizing the beamforming matrix at AF relay and the phase-shift matrices at RIS,two schemes are put forward to address a maximizing signal-to-noise ratio(SNR)problem.First,aiming at achieving a high rate,a high-performance alternating optimization(AO)method based on Charnes–Cooper transformation and semidefinite programming(CCT-SDP)is proposed,where the optimization problem is decomposed into three subproblems solved using CCT-SDP,and rank-one solutions can be recovered using Gaussian randomization.However,the optimization variables in the CCT-SDP method are matrices,leading to extremely high complexity.To reduce the complexity,a low-complexity AO scheme based on Dinkelbachs transformation and successive convex approximation(DT-SCA)is proposed,where the variables are represented in vector form,and the three decoupling subproblems are solved using DT-SCA.Simulation results verify that compared to three benchmarks(i.e.,a RIS-assisted AF relay network with random phase,an AF relay network without RIS,and a RIS-aided network without AF relay),the proposed CCT-SDP and DT-SCA schemes can harvest better rate performance.Furthermore,it is revealed that the rate of the low-complexity DT-SCA method is close to that of the CCT-SDP method.

关键词： Reconfigurable intelligent surface(RIS) Amplify-and-forward(AF)relay Beamforming Phase shift semidefinite programming Successive convex approximation

Unified convergence analysis of a second-order method of multipliers for nonlinear conic programming

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Science China Mathematics 2022年第11期65卷 2397-2422页

作者： Liang Chen Junyuan Zhu Xinyuan Zhao School of Mathematics Hunan UniversityChangsha 410082China Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics Changsha 410082China School of Mathematics Beijing University of TechnologyBeijing 100124China

In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.Specifically,the algorithm that we investigate incorporates a specially designed nonsmooth(generalized)Newton step to furnish a second-order update rule for the multipliers.We first show in a unified fashion that under a few abstract assumptions,the proposed method is locally convergent and possesses a(nonasymptotic)superlinear convergence rate,even though the penalty parameter is fixed and/or the strict complementarity fails.Subsequently,we demonstrate that for the three typical scenarios,i.e.,the classic nonlinear programming,the nonlinear second-order cone programming and the nonlinear semidefinite programming,these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that are assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict complementarity.

关键词： second-order method of multipliers augmented Lagrangian method convergence rate generalized Newton method second-order cone programming semidefinite programming

Successive quadratic programming multiuser detector

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Journal of Systems Engineering and Electronics 2007年第1期18卷 8-13页

作者： Mu Xuewen Zhang Yaling Liu Sanyang Dept. of Applied Mathematics Xidian Univ. Xi'an 710071 E R. China Dept. of Computer Science and Technology Xi'an Univ. of Science and Technology Xi'an 710054 P. R. China

Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem, a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported based on semidefmite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.

关键词： Code division multiple access Multiuser detection semidefinite programming Successive quadratic programming.