Abstract
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.
Highlights
The nonconvex quadratically constrained quadratic programs problems have attracted the attention of practitioners and researchers for 30 years
The optimal value of the problem (PLPRP) offers a valid lower bound for the optimal value of the problem (NQCQP) over the subhyperrectangle X
If γ0p(θ0) < 0, we can prove that the subhyperrectangle Y does not contain the global optimum point of the problem (NQCQP)
Summary
The nonconvex quadratically constrained quadratic programs problems have attracted the attention of practitioners and researchers for 30 years. Many nonlinear optimization problems can be transformed into the form, for example, special classes of structured stochastic games [9] can be interpreted as quadratic programs problems, the packing problem contained in the unit square can be formulated as concave quadratic constraints quadratic programs problem, {0, 1} variable in 0-1 programming may be represented by concave quadratic constraints, and minmax location problems [4] lead to quadratic programs problems with quadratic constraints Another cause for the strong attention in the NQCQP problems is that, from a research point of view, the class of problems put forward significant theoretical and computational defiance. Combing the parametric linear programs relaxation problem with the cutting down approach in a branch and bound procedure, a new optimization method is displayed for globally solving the NQCQP problems.
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