Abstract
This paper presents a novel range division and contraction approach for globally solving nonconvex quadratic program with quadratic constraints. By constructing new underestimating linear relaxation functions, we can transform the initial nonconvex quadratic program problem into a linear program relaxation problem. By employing a branch and bound scheme with a range contraction approach, we describe a novel global optimization algorithm for effectively solving nonconvex quadratic program with quadratic constraints. Finally, the global convergence of the proposed algorithm is proved and numerical experimental results demonstrate the effectiveness of the proposed approach.
Highlights
The mathematical modeling of nonconvex quadratic program with quadratic constraints can be formulated as follows: min F0(x) =xT Q0x + d0T x (NQPQC) : s.t
We denote LB(Xk ) and xk = x(Xk ) as the optimum value and optimal solution of the linear program relaxation problem over the sub-rectangle Xk, respectively. Combining the former linear program relaxation problem, range division method and range contraction approach together, a new global optimization method is constructed for effectively solving the NQPQC, the main steps of the proposed algorithm are described as follows
In this article, a new range division and contraction algorithm is proposed for globally solving nonconvex quadratic program with quadratic constraints (NQPQC)
Summary
The mathematical modeling of nonconvex quadratic program with quadratic constraints can be formulated as follows: min F0(x) =xT Q0x + d0T x (NQPQC) : s.t. Based on parametric linear relaxation and new linearizing technique, Jiao et al (2015), Jiao and Chen (2013) proposed two branch and bound algorithms for globally solving nonconvex quadratic programs.
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