An eigenvalue decomposition based branch-and-bound algorithm for nonconvex quadratic programming problems with convex quadratic constraints

2016 ◽  
Vol 67 (3) ◽  
pp. 475-493 ◽  
Author(s):  
Cheng Lu ◽  
Zhibin Deng ◽  
Qingwei Jin
Keyword(s):  
Quadratic Programming ◽  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Eigenvalue Decomposition ◽  
Nonconvex Quadratic Programming ◽  
Quadratic Constraints ◽  
Quadratic Programming Problems ◽  
Convex Quadratic Constraints

scholarly journals A Branch and Bound Reduced Algorithm for Quadratic Programming Problems with Quadratic Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yuelin Gao ◽  
Feifei Li ◽  
Siqiao Jin
Keyword(s):  
Lower Bound ◽  
Quadratic Programming ◽  
Branch And Bound ◽  
Numerical Experiments ◽  
Original Problem ◽  
Degree Of Approximation ◽  
Quadratic Constraints ◽  
Reduction Strategy ◽  
Optimal Value ◽  
Quadratic Programming Problems

We propose a branch and bound reduced algorithm for quadratic programming problems with quadratic constraints. In this algorithm, we determine the lower bound of the optimal value of original problem by constructing a linear relaxation programming problem. At the same time, in order to improve the degree of approximation and the convergence rate of acceleration, a rectangular reduction strategy is used in the algorithm. Numerical experiments show that the proposed algorithm is feasible and effective and can solve small- and medium-sized problems.

scholarly journals A Global Optimization Algorithm for Generalized Quadratic Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongwei Jiao ◽  
Yongqiang Chen
Keyword(s):  
Linear Programming ◽  
Global Optimization ◽  
Quadratic Programming ◽  
Optimization Algorithm ◽  
Global Minimum ◽  
Nonconvex Programming ◽  
Nonconvex Quadratic Programming ◽  
Global Optimization Algorithm ◽  
Quadratic Constraints ◽  
Linear Programming Problems

We present a global optimization algorithm for solving generalized quadratic programming (GQP), that is, nonconvex quadratic programming with nonconvex quadratic constraints. By utilizing a new linearizing technique, the initial nonconvex programming problem (GQP) is reduced to a sequence of relaxation linear programming problems. To improve the computational efficiency of the algorithm, a range reduction technique is employed in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (GQP) by means of the subsequent solutions of a series of relaxation linear programming problems. Finally, numerical results show the robustness and effectiveness of the proposed algorithm.

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