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Chinese Automation Congress (CAC)

作者： Huang, Chao Zhang, Hao Wang, Zhuping Zhang, Changzhu Tongji Univ Coll Elect & Informat Engn Shanghai Inst Intelligent Sci & Technol Shanghai Peoples R China

ISBN: (纸本)9781728176871

Modern society is a networked society. To design or build a network, one has to consider the cost of building it, the efficiency of transmission of information, resources, energy or man in the network, and the fault tolerance when some nodes and pathways in the network fail. These requirements are often mutually restricted. In order to design optimized network, this paper formulate a novel semi-definite programming (SDP) problem. First, a new objective function is designed, which constitutes of the total network length and the determinant of the network Laplacian. Then, the constraints of the SDP is proposed as the flux rules and node rules of a bio-inspired optimization algorithm. Finally, The proposed algorithm is validated by numerical examples.

关键词： Network optimization Physarum polycephalum semi-definite programming

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Distributed consensus-based solver for semi-definite programming: An optimization viewpoint

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AUTOMATICA 2021年 131卷 109737-109737页

作者： Li, Weijian Zeng, Xianlin Hong, Yiguang Ji, Haibo Univ Sci & Technol China Dept Automat Hefei 230027 Anhui Peoples R China Beijing Inst Technol Sch Automat Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Tongji Univ Dept Control Sci & Engn Shanghai 201804 Peoples R China Shanghai Res Inst Intelligent Syst Shanghai 201203 Peoples R China

This paper aims at the distributed computation for semi-definite programming (SDP) problems over multi-agent networks. Two SDP problems, including a non-sparse case and a sparse case, are transformed into distributed optimization problems, respectively, by fully exploiting their structures and introducing consensus constraints. Inspired by primal-dual and consensus methods, we propose two distributed algorithms for the two cases with the help of projection and derivative feedback techniques. Furthermore, we prove that the algorithms converge to their optimal solutions, and moreover, their convergences rates are evaluated by the duality gap. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Distributed optimization Consensus-based algorithm semi-definite programming Sparsity

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Learning with semi-definite programming: statistical bounds based on fixed point analysis and excess risk curvature

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2021年第1期22卷 10435-10498页

作者： Stéphane Chrétien Mihai Cucuringu Guillaume Lecué Lucie Neirac Université Lyon 2 National Physical Laboratory and The Alan Turing Institute University of Oxford and The Alan Turing Institute CREST ENSAE IPParis

Many statistical learning problems have recently been shown to be amenable to semi-definite programming (SDP), with community detection and clustering in Gaussian mixture models as the most striking instances Javanmard et al. (2016). Given the growing range of applications of SDP-based techniques to machine learning problems, and the rapid progress in the design of efficient algorithms for solving SDPs, an intriguing question is to understand how the recent advances from empirical process theory and Statistical Learning Theory can be leveraged for providing a precise statistical analysis of SDP *** the present paper, we borrow cutting edge techniques and concepts from the Learning Theory literature, such as fixed point equations and excess risk curvature arguments, which yield general estimation and prediction results for a wide class of SDP estimators. From this perspective, we revisit some classical results in community detection from Guédon and Vershynin (2016) and Fei and Chen (2019b), and we obtain statistical guarantees for SDP estimators used in signed clustering, angular group synchronization (for both multiplicative and additive models) and MAX-CUT. Our theoretical findings are complemented by numerical experiments for each of the three problems considered, showcasing the competitiveness of the SDP estimators.

关键词： semi-definite programming statistical learning group Synchronization signed clustering

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An Adaptive Infeasible-Interior-Point Method with the One-Norm Wide Neighborhood for semi-definite programming

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JOURNAL OF SCIENTIFIC COMPUTING 2019年第3期78卷 1790-1810页

作者： Yang, Ximei Bai, Yanqin Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China

In this paper, we present a Mehrotra-type predictor-corrector infeasible-interior-point method, based on the one-norm wide neighborhood, for semi-definite programming. The proposed algorithm uses Mehrotra's adaptive updating scheme for the centering parameter, which incorporates a safeguard strategy that keeps the iterates in a prescribed neighborhood and allows to get a reasonably large step size. Moreover, by using an important inequality that is the relationship between the one-norm and the Frobenius-norm, the convergence is shown for a commutative class of search directions. In particular, the complexity bound is O(nlog epsilon-1) for Nesterov-Todd direction, and O(n3/2log epsilon-1) for Helmberg-Kojima-Monteiro directions, where epsilon is the required precision. The derived complexity bounds coincide with the currently best known theoretical complexity bounds obtained so far for the infeasible semi-definite programming. Some preliminary numerical results are provided as well.

关键词： semi-definite programming Wide neighborhood Adaptive updating scheme Infeasible-interior-point method Complexity bound

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Reachability Estimation of Stochastic Dynamical Systems by semi-definite programming 58

Reachability Estimation of Stochastic Dynamical Systems by S...

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58th IEEE Conference on Decision and Control (CDC)

作者： Liu, Kairong Li, Meilun She, Zhikun Beihang Univ LMIB Beijing Peoples R China Beihang Univ Sch Math & Syst Sci Beijing Peoples R China

ISBN: (纸本)9781728113982

In this paper we present a semi-definite programming based computational method for reachability analysis of stochastic dynamical systems, in which the reachability is characterized by first passage time distribution. Starting from Feynman-Kac formula, we provide over and under approximations of staying probability in a given safety area with explicit algebraical expressions, respectively. Successively, we transform the estimates of over and under approximations into constraint satisfaction problems, which can then be solved efficiently in virtue of SOS programming and global optimization. Two examples are used to show the utility of our method.

关键词： Reachability analysis stochastic dynamical systems semi-definite programming

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Application research on semi-definite programming optimized support vector machines

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IMAGING SCIENCE JOURNAL 2018年第3期66卷 160-168页

作者： Hou, Jingzhong Xia, Kewen Yang, Fan Hebei Univ Technol Sch Elect & Informat Engn Tianjin Peoples R China

The kernel function optimization is the key issues to address when using the support vector machine (SVM) algorithm. To solve the parameter selection for the SVM, a semi-definite programming optimized SVM (SDP-SVM) algorithm is proposed in this paper. The steps of the algorithm are described, and the optimization of the kernel function is shown using an SDP method. The SDP method is used to find the best parameter of SVM. The heart_scale data in the University of California Irvine database are then simulated using the SDP-SVM model. The experimental results shows that the generalization capability and the classification accuracy of the SDP-SVM algorithm have been greatly improved. A variety of strip-steel surface defect images from actual production are classified using the SDP-SVM algorithm, and the results show that the classification method of the SDP-SVM algorithm has high classification accuracy, strong practicability, and a wide variety of application prospects.

关键词： Support vector machines semi-definite programming kernel function strip-steel defect image

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Application research on semi-definite programming optimized support vector machines

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The Journal of Photographic Science 2018年第3期66卷 160-168页

ABSTRACTABSTRACTThe kernel function optimization is the key issues to address when using the support vector machine (SVM) algorithm. To solve the parameter selection for the SVM, a semi-definite programming optimized SVM (SDP-SVM) algorithm is proposed in this paper. The steps of the algorithm are described, and the optimization of the kernel function is shown using an SDP method. The SDP method is used to find the best parameter of SVM. The heart_scale data in the University of California Irvine database are then simulated using the SDP-SVM model. The experimental results shows that the generalization capability and the classification accuracy of the SDP-SVM algorithm have been greatly improved. A variety of strip-steel surface defect images from actual production are classified using the SDP-SVM algorithm, and the results show that the classification method of the SDP-SVM algorithm has high classification accuracy, strong practicability, and a wide variety of application prospects.

关键词： Support vector machines semi-definite programming kernel function strip-steel defect image

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UPPER BOUND PERFORMANCE OF semi-definite programming FOR LOCALISATION IN INHOMOGENEOUS MEDIA

UPPER BOUND PERFORMANCE OF SEMI-DEFINITE PROGRAMMING FOR LOC...

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27th IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

作者： Nadimi, E. S. Blanes-Vidal, V. Univ Southern Denmark Maersk Mc Kinney Moller Inst Embodied Syst Robot & Learning Campusvej 55 DK-5230 Odense Denmark

ISBN: (纸本)9781509063413

In this paper, we regarded an absorbing inhomogeneous medium as an assembly of thin layers having different propagation properties. We derived a stochastic model for the refractive index and formulated the localisation problem given noisy distance measurements using graph realisation problem. We relaxed the problem using semi-definite programming (SDP) approach in l(p) realisation domain and derived upper bounds that follow Edmundson-Madansky bound of order 6p (EM6p) on the SDP objective function to provide an estimation of the techniques' localisation accuracy. Our results showed that the inhomogeneity of the media and the choice of l(p) norm have significant impact on the ratio of the expected value of the localisation error to the upper bound for the expected optimal SDP objective value. The tightest ratio was derived when l(infinity) norm was used.

关键词： semi-definite programming inhomogeneous media localisation Edmundson-Madansky bound

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A semi-definite programming Approach for Solving Optimal Reactive Power Reserve Dispatch

A Semi-definite Programming Approach for Solving Optimal Rea...

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IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC)

作者： Liu, Yuquan Xia, Wen Bo Zheng, Shunqi Wang, Ke Wu, Peng Fang, Sidun Guangzhou Power Supply Co Dept Elect Power Designing Guangzhou Guangdong Peoples R China Shanghai Jiao Tong Univ Dept Elect Engn Shanghai Peoples R China

ISBN: (纸本)9781538613795

It is well known that proper reactive power reserve (RPR) is essential to avoid voltage instability and abnormal voltage. Most literatures limits the maximum supply of generator reactive power output by the maximum loading point. Thus the optimization of RPR usually involves two operating points, i.e. current operating point and maximum loading point. However, extreme differences exist between the statuses of generators at those two operating points and cannot be given in advance. That means current techniques cannot solve optimal RPR model directly. In this paper, a semi-definite programming (SDP) approach for solving optimal RPR model is proposed. Proposed method transforms the solution into iterations and each iteration is an optimal power flow problem solved by SDP. For demonstrating the validity of proposed method, IEEE 118 system in three load scenarios is set as the test case. The results prove the effectiveness and robustness of the proposed method.

关键词： semi-definite programming optimal reactive power reserve dispatch current operating point maximum loading point

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semi-definite programming Approach to Stochastic Combined Heat and Power Environmental/Economic Dispatch Problem

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2015年第18期43卷 2039-2049页

作者： Jubril, Abimbola Muhideen Adediji, Adeyinka Olugbenga Obafemi Awolowo Univ Dept Elect & Elect Engn Ife 220005 Nigeria

This article presents a solution to the stochastic multi-objective combined heat and power environmental/economic dispatch problem using the semi-definite programming formulation. The vector objective is reduced to an equivalent scalar objective using the weighted sum method. The resulting optimization problem is formulated as a convex optimization via semi-definite programming relaxation. The convex optimization problem was solved to obtain Pareto-optimal solutions. Improvement in the distribution of solution set was achieved through non-linear selection of the weight factor. Simulation was performed on a test problem to investigate the effectiveness of the proposed approach. Results showed that the semi-definite programming based weighted sum method has inherently good convergence property and can have its diversity property improved through weight adaptation.

关键词： cogeneration economic dispatch emission dispatch multi-objective optimization semi-definite programming weighted sum method non-linear weighted sum method combined heat and power stochastic programming

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