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

2005 ◽  
Vol 103 (2) ◽  
pp. 251-282 ◽  
Author(s):  
Jeff Linderoth
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Quadratic Programs ◽  
Quadratically Constrained

scholarly journals A Novel Optimization Method for Nonconvex Quadratically Constrained Quadratic Programs

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hongwei Jiao ◽  
Yong-Qiang Chen ◽  
Wei-Xin Cheng
Keyword(s):  
Branch And Bound ◽  
Computational Efficiency ◽  
Numerical Experiments ◽  
Optimization Method ◽  
Global Optimum ◽  
Branch And Bound Algorithm ◽  
Linear Programs ◽  
Quadratic Programs ◽  
Optimum Point ◽  
Quadratically Constrained

This paper presents a novel optimization method for effectively solving nonconvex quadratically constrained quadratic programs (NQCQP) problem. By applying a novel parametric linearizing approach, the initial NQCQP problem and its subproblems can be transformed into a sequence of parametric linear programs relaxation problems. To enhance the computational efficiency of the presented algorithm, a cutting down approach is combined in the branch and bound algorithm. By computing a series of parametric linear programs problems, the presented algorithm converges to the global optimum point of the NQCQP problem. At last, numerical experiments demonstrate the performance and computational superiority of the presented algorithm.

scholarly journals A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs

2008 ◽  
Vol 20 (3) ◽  
pp. 438-450 ◽  
Author(s):  
Juan Pablo Vielma ◽  
Shabbir Ahmed ◽  
George L. Nemhauser
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Mixed Integer ◽  
Quadratic Programs

scholarly journals Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

2017 ◽  
Vol 15 (1) ◽  
pp. 1212-1224 ◽  
Author(s):  
Zhisong Hou ◽  
Hongwei Jiao ◽  
Lei Cai ◽  
Chunyang Bai
Keyword(s):  
Branch And Bound ◽  
Computational Efficiency ◽  
Global Minimum ◽  
Quadratic Function ◽  
Numerical Results ◽  
Linear Programs ◽  
Quadratic Programs ◽  
New Variables ◽  
Quadratically Constrained ◽  
Methods Numerical

Abstract This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound framework without introducing any new variables and constrained functions, which can be easily solved by any effective linear programs algorithms. By subsequently solving a series of linear relaxed programs problems, the proposed algorithm can converge the global minimum of the initial quadratically constrained quadratic programs problem. Compared with the known methods, numerical results demonstrate that the proposed method has higher computational efficiency.

Perspective Reformulations of Semicontinuous Quadratically Constrained Quadratic Programs

2020 ◽  
Author(s):  
Xiaojin Zheng ◽  
Yutong Pan ◽  
Zhaolin Hu
Keyword(s):  
Lower Bounds ◽  
Branch And Bound ◽  
Strong Duality ◽  
Computational Experiments ◽  
Quadratic Programs ◽  
Branch And Bound Algorithms ◽  
Study Perspective ◽  
Lifting Techniques ◽  
Quadratically Constrained

We study perspective reformulations (PRs) of semicontinuous quadratically constrained quadratic programs (SQCQPs) in this paper. Based on perspective functions, we first propose a class of PRs for SQCQPs and discuss how to find the best PR in this class via strong duality and lifting techniques. We then study the properties of the PR class and relate them to alternative formulations that are used to derive lower bounds for SQCQPs. Finally, we embed the PR bounds in branch-and-bound algorithms and conduct computational experiments to illustrate the effectiveness of the proposed approach.

Unit Commitment Solution by Branch and Bound Algorithm

2020 ◽  
Author(s):  
Bishaljit Paul ◽  
Sushovan Goswami ◽  
Dipu Mistry ◽  
Chandan Kumar Chanda
Keyword(s):  
Branch And Bound ◽  
Unit Commitment ◽  
Branch And Bound Algorithm
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