检索结果-内蒙古大学图书馆

An interior point method for general large-scale quadratic programming problems

ANNALS OF OPERATIONS RESEARCH 1996年第1期62卷 419-437页

作者： Boggs, PT Domich, PD Rogers, JE NATL INST STAND & TECHNOL APPL & COMPUTAT MATH DEPTGAITHERSBURGMD 20899 NATL INST STAND & TECHNOL APPL & COMPUTAT MATH DEPTBOULDERCO 80303

In this paper, we present an interior point algorithm for solving both convex and nonconvex quadratic programs. The method, which is an extension of our interior point work on linear programming problems, efficiently solves a wide class of large-scale problems and forms the basis for a sequential quadratic programming (SQP) solver for general large scale nonlinear programs. The key to the algorithm is a three-dimensional cost improvement subproblem, which is solved at every iteration. We have developed an approximate recentering procedure and a novel, adaptive big-M Phase I procedure that are essential to the success of the algorithm. We describe the basic method along with the recentering and big-M Phase I procedures. Details of the implementation and computational results are also presented.

关键词： big-M Phase I procedure convex quadratic programming interior point methods linear programming method of centers multidirectional search direction nonconvex quadratic programming recentering

来源：评论

学校读者我要写书评

暂无评论

Finding largest small polygons with GloptiPoly

引用

JOURNAL OF GLOBAL OPTIMIZATION 2013年第3期56卷 1017-1028页

作者： Henrion, Didier Messine, Frederic CNRS LAAS F-31077 Toulouse France Univ Toulouse UPS INSA INPISAEUT1UTMLAAS F-31077 Toulouse France Czech Tech Univ Fac Elect Engn Prague 16626 Czech Republic Univ Toulouse ENSEEIHT IRIT F-31071 Toulouse France

A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices n. Many instances are already solved in the literature, namely for all odd n, and for n = 4, 6 and 8. Thus, for even n a parts per thousand yen 10, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic programming problems which can challenge state-of-the-art global optimization algorithms. We show that a recently developed technique for global polynomial optimization, based on a semidefinite programming approach to the generalized problem of moments and implemented in the public-domain Matlab package GloptiPoly, can successfully find largest small polygons for n = 10 and n = 12. Therefore this significantly improves existing results in the domain. When coupled with accurate convex conic solvers, GloptiPoly can provide numerical guarantees of global optimality, as well as rigorous guarantees relying on interval arithmetic.

关键词： Extremal convex polygons Global optimization nonconvex quadratic programming Semidefinite programming

来源：评论

学校读者我要写书评

暂无评论

A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs

引用

MATHEMATICAL programming 2005年第2期103卷 251-282页

作者： Linderoth, J Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA

We propose a branch-and-bound algorithm for solving nonconvex quadratically-constrained quadratic programs. The algorithm is novel in that branching is done by partitioning the feasible region into the Cartesian product of two-dimensional triangles and rectangles. Explicit formulae for the convex and concave envelopes of bilinear functions over triangles and rectangles are derived and shown to be second-order cone representable. The usefulness of these new relaxations is demonstrated both theoretically and computationally.

关键词： nonconvex quadratic programming global optimization convex envelope branch-and-bound

来源：评论

学校读者我要写书评

暂无评论

Nonlinear Energy Arbitrage Models and Algorithms for Battery Energy Storage Systems in Electricity Market

Nonlinear Energy Arbitrage Models and Algorithms for Battery...

引用

North American Power Symposium (NAPS)

作者： Li, Ang Peng, Jiming Fan, Lei Du, Pengwei Univ Houston Dept Ind Engn Houston TX 77004 USA Univ Houston Dept Engn Technol Houston TX 77004 USA Elect Reliabil Council Texas Austin TX USA

ISBN: (纸本)9798350315097

Battery energy storage systems (BESSs) are gaining attention due to reduced costs and high flexibility, but developing accurate models for operation presents challenges. This paper introduces a model for the charging and discharging processes via a single current decision variable, approximates the relation between the open circuit voltage and the state of charge with linear functions, and presents an optimization model with bilinear constraints for identifying optimal BESS operational strategies. A transformation technique is introduced to manage the bilinear constraints, transforming the model into an exponential optimization problem with linear constraints. A new sequential linear and quadratic programming approach is developed, with proven convergence. Preliminary experiments demonstrate the efficacy and efficiency of this approach.

关键词： Battery Energy Storage Electricity Market Energy Arbitrage Model nonconvex quadratic programming

来源：评论

学校读者我要写书评

暂无评论

A New Branch and Bound Algorithm for Noncovex quadratic programming with Box Constraints

A New Branch and Bound Algorithm for Noncovex Quadratic Prog...

引用

10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

作者： Fu, Wenlong Du, Tingsong China Three Gorges Univ Coll Sci Inst Nonlinear & Complex Syst Yichang 443002 Peoples R China

ISBN: (纸本)9781467352536

In this paper, we investigate a class of nonconvex quadratic programming with box constrains. A new branch and bound algorithm is proposed. The improvement of the new method is how to determine the lower bound. We put nonconvex quadratic programming into convex quadratic programming, and get an optimal solution as lower bound of original problem. Meanwhile, an upper bound is got by existing methods. Moreover, by used of the branch and bound algorithm, we can solve the original problem by solved a series of subproblems. Finally, the convergence of the proposed new algorithm is proved.

关键词： nonconvex quadratic programming box constrainted branch and bound algorithm

来源：评论

学校读者我要写书评

暂无评论

Finding largest small polygons with GloptiPoly

Finding largest small polygons with GloptiPoly

引用

Global Optimization Workshops (GOWs)

关键词： Extremal convex polygons Global optimization nonconvex quadratic programming Semidefinite programming

来源：评论

学校读者我要写书评

暂无评论

On the solution of indefinite quadratic problems using an interior-point algorithm

引用

Informatica (Netherlands) 1992年第4期3卷 474-496页

作者： Han, Chi-Geun Pardalos, Panos M. Ye, Yinyu Computer Science Department The Pennsylvania State University University Park PA 16802 United States Department of Industrial and Systems Engineering University of Florida Gainesville FL 32611 United States Department of Management Sciences The University of Iowa Iowa City IA 52242 United States

In/this paper, we discuss computational aspects of an interior- point algorithm [1] for indefinite quadratic programming problems with box constraints. The algorithm finds a local minimizer by successively solving indefinite quadratic problems with an ellipsoid constraint. In addition, we present a sufficient condition* for a local minimizer to be global, and we use this result to generate test problems with a known global solution. The proposed algorithm has been implemented on an IBM 3090 computer and tested on a variety of dense test problems, including problems with a known global optimizer. © 1992 Institute of Mathematics and Informatics.

关键词： Computational testing Interior point algorithms nonconvex quadratic programming

来源：评论

学校读者我要写书评

暂无评论

Continuity and Directional Differentiability of the Value Function in Parametric quadratically Constrained nonconvex quadratic Programs

引用

ACTA MATHEMATICA VIETNAMICA 2017年第2期42卷 311-336页

作者： Tran Van Nghi Nguyen Nang Tam Hanoi Pedag Univ 2 Hanoi Vietnam

The aim of this paper is to investigate the continuity and the directional differentiability of the value function in quadratically constrained nonconvex quadratic programming problem. Our result can be used in some cases where the existing results on differential stability in nonlinear programming (applied to quadratic programming) cannot be used.

关键词： nonconvex quadratic programming quadratically constrained Value function Continuity Directional differentiability

来源：评论

学校读者我要写书评

暂无评论

PROBABILISTIC MATRIX COMPLETION FOR IMAGE PHASE RETRIEVAL 25

PROBABILISTIC MATRIX COMPLETION FOR IMAGE PHASE RETRIEVAL

引用

25th IEEE International Conference on Image Processing (ICIP)

作者： Nyfantis, Petros Ruiz, Pablo Katsaggelos, Aggelos K. Univ Athens Dept Phys Athens Greece Northwestern Univ Dept Elect Engn & Comp Sci Evanston IL 60208 USA

ISBN: (纸本)9781479970612

In this paper we address the Phase Retrieval problem, which aims to recover the phase of the Fourier transform of a signal when only magnitude measurements are available. Following recent developments in Phase Retrieval, the problem can be transformed into a convex semidefinite programming optimization problem, which can be solved using Matrix Completion techniques. In this paper the acquisition process is modeled using a likelihood function, which splits the original problem into two convex optimization problems, and alternates between the solution of each of them. To relate both convex problems we introduce a heuristic, which results in fast convergence of the proposed method.

关键词： Phase retrieval lifting nonconvex quadratic programming alternating minimization

来源：评论

学校读者我要写书评

暂无评论

Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs

引用

OPTIMIZATION METHODS & SOFTWARE 2009年第4-5期24卷 485-504页

作者： Bao, Xiaowei Sahinidis, Nikolaos V. Tawarmalani, Mohit Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Univ Illinois Dept Chem & Biomol Engn Urbana IL 61801 USA Purdue Univ Krannert Sch Management W Lafayette IN 47907 USA

This article addresses the generation of strong polyhedral relaxations for nonconvex, quadratically constrained quadratic programs (QCQPs). Using the convex envelope of multilinear functions as our starting point, we develop a polyhedral relaxation for QCQP, along with a cutting plane algorithm for its implementation. Our relaxations are multiterm, i.e. they are derived from the convex envelope of the sum of multiple bilinear terms of quadratic constraints, thereby providing tighter bounds than the standard termwise relaxation of the bilinear functions. Computational results demonstrate the usefulness of the proposed cutting planes.

关键词： nonconvex quadratic programming polyhedral relaxation convex envelope cutting plane global optimization

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：