Decomposition Methods for Solving Nonconvex Quadratic Programs via Branch and Bound*

2005 ◽  
Vol 33 (3) ◽  
pp. 313-336 ◽  
Author(s):  
Riccardo Cambini ◽  
Claudio Sodini
Keyword(s):  
Branch And Bound ◽  
Decomposition Methods ◽  
Quadratic Programs

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 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 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.

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