检索结果-内蒙古大学图书馆

quadratically constrained quadratic programming Formulation of Contingency constrained Optimal Power Flow with Photovoltaic Generation

引用

ENERGIES 2020年第13期13卷 3310页

作者： Leon, Luis M. Bretas, Arturo S. Rivera, Sergio Univ Nacl Colombia Sede Bogota Elect & Elect Engn Bogota 111321 Colombia Univ Florida Elect & Comp Engn Dept Gainesville FL 32611 USA

Contingency constrained Optimal Power Flow (CCOPF) differs from traditional Optimal Power Flow (OPF) because its generation dispatch is planned to work with state variables between constraint limits, considering a specific contingency. When it is not desired to have changes in the power dispatch after the contingency occurs, the CCOPF is studied with a preventive perspective, whereas when the contingency occurs and the power dispatch needs to change to operate the system between limits in the post-contingency state, the problem is studied with a corrective perspective. As current power system software tools mainly focus on the traditional OPF problem, having the means to solve CCOPF will benefit power systems planning and operation. This paper presents a quadratically constrained quadratic programming (QCQP) formulation built within thematpowerenvironment as a solution strategy to the preventive CCOPF. Moreover, an extended OPF model that forces the network to meet all constraints under contingency is proposed as a strategy to find the power dispatch solution for the corrective CCOPF. Validation is made on the IEEE 14-bus test system including photovoltaic generation in one simulation case. It was found that in the QCQP formulation, the power dispatch calculated barely differs in both pre- and post-contingency scenarios while in the OPF extended power network, node voltage values in both pre- and post-contingency scenarios are equal in spite of having different power dispatch for each scenario. This suggests that both the QCQP and the extended OPF formulations proposed, could be implemented in power system software tools in order to solve CCOPF problems from a preventive or corrective perspective.

关键词： quadratically constrained quadratic programming contingency constrained optimal power flow optimal power flow

来源：评论

学校读者我要写书评

暂无评论

Convex relaxations for nonconvex quadratically constrained quadratic programming: matrix cone decomposition and polyhedral approximation

引用

MATHEMATICAL programming 2011年第2期129卷 301-329页

作者： Zheng, Xiao Jin Sun, Xiao Ling Li, Duan Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China Fudan Univ Sch Management Dept Management Sci Shanghai 200433 Peoples R China

We present a decomposition-approximation method for generating convex relaxations for nonconvex quadratically constrained quadratic programming (QCQP). We first develop a general conic program relaxation for QCQP based on a matrix decomposition scheme and polyhedral (piecewise linear) underestimation. By employing suitable matrix cones, we then show that the convex conic relaxation can be reduced to a semidefinite programming (SDP) problem. In particular, we investigate polyhedral underestimations for several classes of matrix cones, including the cones of rank-1 and rank-2 matrices, the cone generated by the coefficient matrices, the cone of positive semidefinite matrices and the cones induced by rank-2 semidefinite inequalities. We demonstrate that in general the new SDP relaxations can generate lower bounds at least as tight as the best known SDP relaxations for QCQP. Moreover, we give examples for which tighter lower bounds can be generated by the new SDP relaxations. We also report comparison results of different convex relaxation schemes for nonconvex QCQP with convex quadratic/linear constraints, nonconvex quadratic constraints and 0-1 constraints.

关键词： quadratically constrained quadratic programming Convex relaxation Decomposition-approximation method Polyhedral approximation Semidefinite programming Rank-2 semidefinite inequalities

来源：评论

学校读者我要写书评

暂无评论

A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第1-2期220卷 525-547页

作者： Tang, Chun-Ming Jian, Jin-Bao Guangxi Univ Coll Math & Informat Sci Nanning 530004 Peoples R China Shanghai Univ Dept Math Shanghai Peoples R China

Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered. (c) 2007 Published by Elsevier B.V.

关键词： SQCQP quadratically constrained quadratic programming augmented Lagrangian line search function nonlinear programming convergence

来源：评论

学校读者我要写书评

暂无评论

Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions

引用

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期200卷 645-657页

作者： Jian, Jin-Bao Tang, Chun-Ming Zheng, Hai-Yan Guangxi Univ Coll Math & Informat Sci Nanning 530004 Peoples R China

In this paper, we present a sequential quadratically constrained quadratic programming (SQCQP) norm-relaxed algorithm of strongly sub-feasible directions for the solution of inequality constrained optimization problems. By introducing a new unified line search and making use of the idea of strongly sub-feasible direction method, the proposed algorithm can well combine the phase of finding a feasible point (by finite iterations) and the phase of a feasible descent norm-relaxed SQCQP algorithm. Moreover, the former phase can preserve the "sub-feasibility" of the current iteration, and control the increase of the objective function. At each iteration, only a consistent convex quadratically constrained quadratic programming problem needs to be solved to obtain a search direction. Without any other correctional directions, the global, superlinear and a certain quadratic convergence (which is between 1-step and 2-step quadratic convergence) properties are proved under reasonable assumptions. Finally, some preliminary numerical results show that the proposed algorithm is also encouraging. (C) 2009 Published by Elsevier B.V.

关键词： Optimization quadratically constrained quadratic programming SQCQP superlinear convergence Norm-relaxed algorithm

来源：评论

学校读者我要写书评

暂无评论

Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming

引用

JOURNAL OF GLOBAL OPTIMIZATION 2009年第2-3期43卷 471-484页

作者： Anstreicher, Kurt M. Univ Iowa Dept Management Sci Tippie Coll Business Iowa City IA 52242 USA

We consider relaxations for nonconvex quadratically constrained quadratic programming (QCQP) based on semidefinite programming (SDP) and the reformulation-linearization technique (RLT). From a theoretical standpoint we show that the addition of a semidefiniteness condition removes a substantial portion of the feasible region corresponding to product terms in the RLT relaxation. On test problems we show that the use of SDP and RLT constraints together can produce bounds that are substantially better than either technique used alone. For highly symmetric problems we also consider the effect of symmetry-breaking based on tightened bounds on variables and/or order constraints.

关键词： Semidefinite programming Reformulation-linearization technique quadratically constrained quadratic programming

来源：评论

学校读者我要写书评

暂无评论

New bounds for nonconvex quadratically constrained quadratic programming

引用

JOURNAL OF GLOBAL OPTIMIZATION 2023年第3期85卷 595-613页

作者： Zamani, Moslem Tilburg Univ Dept Econometr & Operat Res Tilburg Netherlands

In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs (QCQPs). We propose two types of bounds for QCQPs, quadratic and cubic bounds. We use affine functions as Lagrange multipliers for quadratic bounds. We demonstrate that most semidefinite relaxations can be obtained as the dual of a quadratic bound. In addition, we study bounds obtained by changing the ground set. For cubic bounds, in addition to affine multipliers we employ quadratic functions. We provide a comparison between the proposed cubic bound and typical bounds for standard quadratic programs. Moreover, we report comparison results of some quadratic and cubic bounds.

关键词： quadratically constrained quadratic programming Semidefinite relaxation Reformulation-linearization technique

来源：评论

学校读者我要写书评

暂无评论

On the sequential quadratically constrained quadratic programming methods

引用

MATHEMATICS OF OPERATIONS RESEARCH 2004年第1期29卷 64-79页

作者： Solodov, MV Inst Matematica Pura & Aplicada BR-22460320 Rio De Janeiro Brazil

An iteration of the sequential quadratically constrained quadratic programming method (SQCQP) consists of minimizing a quadratic approximation of the objective function subject to quadratic approximation of the constraints, followed by a line search in the obtained direction. Methods of this class are receiving attention due to the development of efficient interior point techniques for solving subproblems with this structure, via formulating them as second-order cone programs. Recently, Fukushima et al. (2003) proposed a SQCQP method for convex minimization with twice continuously differentiable data. Their method possesses global and locally quadratic convergence, and it is free of the Maratos effect. The feasibility of subproblems in their method is enforced by switching between the linear and quadratic approximations of the constraints. This strategy requires computing a strictly feasible point, as well as choosing some further parameters. We propose a SQCQP method where feasibility of subproblems is ensured by introducing a slack variable and, hence, is automatic. In addition, we do not assume convexity of the objective function or twice differentiability of the problem data. While our method has all the desirable convergence properties, it is easier to implement. Among other things, it does not require computing a strictly feasible point, which is a nontrivial task. In addition, its global convergence requires weaker assumptions.

关键词： quadratically constrained quadratic programming nonsmooth penalty function Maratos effect

来源：评论

学校读者我要写书评

暂无评论

A Novel quadratically constrained quadratic programming Method for Optimal Coordination of Directional Overcurrent Relays

引用

IEEE TRANSACTIONS ON POWER DELIVERY 2017年第1期32卷 3-10页

作者： Papaspiliotopoulos, Vasileios A. Korres, George N. Maratos, Nicholas G. Natl Tech Univ Athens Sch Elect & Comp Engn Athens 15780 Greece

The coordination of directional overcurrent relays (DOCRs) in meshed power grids with multiple sources is a constrained optimization problem, which has been stated in recent literature as linear (LP), nonlinear (NLP), and mixed-integer nonlinear programming (MINLP) problem. In this paper, the DOCR coordination NLP problem is reformulated as an equivalent quadratically constrained quadratic programming (QCQP) model, leading to significant reduction of problem complexity. Another contribution of this work is the systematic problem statement using graph theory concepts. The proposed method is applied to three different meshed power systems, employing state-of-the-art optimization software. Simulation results demonstrate the efficacy and superiority of the proposed QCQP model over the prevailing NLP approach.

关键词： Directional overcurrent relays nonlinear programming pickup current setting power system protection quadratically constrained quadratic programming relay coordination time dial setting

来源：评论

学校读者我要写书评

暂无评论

Semidefinite approximation bound for a class of nonhomogeneous nonconvex quadratically constrained quadratic programming problem

引用

OPTIMIZATION LETTERS 2019年第4期13卷 837-845页

作者： Xu, Zi Tao, Siqi Lou, Kaiyao Shanghai Univ Dept Math Shanghai 200444 Peoples R China

In this paper, we consider a class of nonconvex nonhomogeneous quadratically constrained quadratic optimization problem. We derive some sufficient condition for the input data, and then establish a semi-definite approximation bound based on a randomization algorithm. The approximation bound is optimal in the order of m in general under the given restriction on the input data.

关键词： quadratically constrained quadratic programming Semidefinite programming relaxation Approximation algorithm

来源：评论

学校读者我要写书评

暂无评论

KKT SOLUTION AND CONIC RELAXATION FOR SOLVING quadratically constrained quadratic programming PROBLEMS

引用

SIAM JOURNAL ON OPTIMIZATION 2011年第4期21卷 1475-1490页

作者： Lu, Cheng Fang, Shu-Cherng Jin, Qingwei Wang, Zhenbo Xing, Wenxun Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China N Carolina State Univ Dept Ind & Syst Engn Raleigh NC 27606 USA

To find a global optimal solution to the quadratically constrained quadratic programming problem, we explore the relationship between its Lagrangian multipliers and related linear conic programming problems. This study leads to a global optimality condition that is more general than the known positive semidefiniteness condition in the literature. Moreover, we propose a computational scheme that provides clues of designing effective algorithms for more solvable quadratically constrained quadratic programming problems.

关键词： quadratically constrained quadratic programming conic programming global optimality condition solvable condition

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：