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Exact Computable Representation of Some second-order cone Constrained Quadratic Programming Problems

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Journal of the Operations Research Society of China 2013年第1期1卷 107-134页

作者： Qingwei Jin Ye Tian Zhibin Deng Shu-Cherng Fang Wenxun Xing Department of Management Science and Engineering Zhejiang UniversityHangzhou310058China School of Business Administration Southwestern University of Finance and EconomicsChengdu611130China Edward P.Fitts Department of Industrial and Systems Engineering North Carolina State UniversityRaleighNC 27695USA Department of Mathematical Sciences Tsinghua UniversityBeijing100084China

Solving the quadratically constrained quadratic programming(QCQP)problem is in general *** a few subclasses of the QCQP problem are known to be polynomial-time ***,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone *** this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints.

关键词： Linear conic program Semidefinite program Nonconvex quadratically constrained quadratic program second-order cone

Quadratic Optimization over a second-order cone with Linear Equality Constraints

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Journal of the Operations Research Society of China 2014年第1期2卷 17-38页

作者： Xiao-ling Guo Zhi-bin Deng Shu-Cherng Fang Zhen-bo Wang Wen-xun Xing Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China Industrial and Systems Engineering Department North Carolina State UniversityRaleighNC 27695USA

This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality *** the feasible region is bounded,we show that an optimal solution of the problem can be found in polynomial *** the feasible region is unbounded,a semidefinite programming(SDP)reformulation is constructed to find the optimal objective value of the original problem in polynomial *** addition,we provide two sufficient conditions,under which,if the optimal objective value is finite,we show the optimal solution of SDP reformulation can be decomposed into the original space to generate an optimal solution of the original problem in polynomial ***,a recession direction can be identified in polynomial *** examples are included to illustrate the effectiveness of the proposed approach.

关键词： Quadratic programming Linear conic programming second-order cone cone of nonnegative quadratic functions

A Class of second-order cone Eigenvalue Complementarity Problems for Higher-order Tensors

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Journal of the Operations Research Society of China 2017年第1期5卷 45-64页

作者： Jiao-Jiao Hou Chen Ling Hong-Jin He Department of Mathematics School of ScienceHangzhou Dianzi UniversityHangzhou 310018China

In this paper,we consider the second-order cone tensor eigenvalue complementarity problem(SOCTEiCP)and present three different reformulations to the model under ***,for the general SOCTEiCP,we first show its equivalence to a particular variational inequality under reasonable conditions.A notable benefit is that such a reformulation possibly provides an efficient way for the study of properties of the ***,for the symmetric and sub-symmetric SOCTEiCPs,we reformulate them as appropriate nonlinear programming problems,which are extremely beneficial for designing reliable solvers to find solutions of the considered ***,we report some preliminary numerical results to verify our theoretical results.

关键词： Higher-order tensor Eigenvalue complementarity problem Tensor complementarity problem second-order cone Variational inequality Polynomial optimization

Controlled Islanding Strategy Considering Uncertainty of Renewable Energy Sources Based on Chance-constrained Model

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Journal of Modern Power Systems and Clean Energy 2022年第2期10卷 471-481页

作者： Shengyuan Liu Tianhan Zhang Zhenzhi Lin Yilu Liu Yi Ding Li Yang the School of Electrical Engineering Zhejiang UniversityHangzhou 310027China the Department of Electrical Engineering and Computer Science University of TennesseeKnoxvilleTN 37996USA the School of Electrical Engineering Shandong UniversityJinan 250061China Electrical and Electronics Systems Research Division Oak Ridge National LaboratoryOak RidgeTN 37830USA

Controlled islanding plays an essential role in preventing the blackout of power *** there are several studies on this topic in the past,no enough attention is paid to the uncertainty brought by renewable energy sources(RESs)that may cause unpredictable unbalanced power and the observabilit>T of power systems after islanding that is essential for back-up black-start ***,a novel controlled islanding model based on mixed-integer second-order cone and chance-constrained programming(MISOCCP)is proposed to address these ***,the uncertainty of RESs is characterized by their possibility distribution models with chance constraints,and the requirements,e.g.,system observability,for rapid back-up black-start measures are also ***,a law of large numbers(LLN)based method is em-ployed for converting the chance constraints into deterministic ones and reformulating the non-convex model into convex ***,case studies on the revised IEEE 39-bus and 118-bus power systems as well as the comparisons among different models are given to demonstrate the effectiveness of the proposed *** results show that the proposed model can result in less unbalanced power and better observability after islanding compared with other models.

关键词： Controlled islanding second-order cone chance-constrained programming renewable energy source(RES) black-start observability.

Robust Optimal Operation of Active Distribution Network Based on Minimum Confidence Interval of Distributed Energy Beta Distribution

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Journal of Modern Power Systems and Clean Energy 2021年第2期9卷 423-430页

作者： Yanhong Luo Qiubo Nie Dongsheng Yang Bowen Zhou the Department of Electric Engineering Northeastern UniversityShenyang 110004China

With the gradual increase of distributed energy penetration,the traditional optimization model of distribution network can no longer guarantee the stable and efficient operation of the distribution *** order to deal with the inevitable uncertainty of distributed energy,a new robust optimal operation method is proposed for active distribution network(ADN)based on the minimum confidence interval of distributed energy Beta distribution in this ***,an ADN model is established with second-order cone to include the energy storage device,capacitor bank,static var compensator,on-load tap changer,wind turbine and ***,the historical data of related distributed energy are analyzed and described by the probability density function,and the minimum confidence interval is obtained by interval ***,via taking this minimum confidence interval as the uncertain interval,a less conservative two-stage robust optimization model is established and solved for *** simulation results for the IEEE33-bus distribution network have verified that the proposed method can realize a more stable and efficient operation of the distribution network compared with the traditional robust optimization method.

关键词： Active distribution network robust optimization Beta distribution second-order cone

A Modified Newton Method Based on the Metric Projector for Solving SOCCVI Problem

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Journal of Applied Mathematics and Physics 2022年第4期10卷 1036-1054页

作者： Hao Liu Juhe Sun Li Wang School of Science Shenyang Aerospace University Shenyang China

In this paper, based on the second-order sufficient condition, the Clarke's generalized Jacobian of the Karush-Kuhn-Tucker system of the second-order cone constrained variational inequality (SOCCVI) problem that is nonsingular is proved by us. A modified Newton method with Armijo line search is presented. Three illustrative examples are given to show how the modified Newton method works.

关键词： second-order cone Variational Inequality Metric Projector second-order Sufficient Condition