An integral function and vector sequence method for unconstrained global optimization |
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| Authors: | Yongjian Yang Fusheng Bai |
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| Affiliation: | (3) Air Force Research Laboratory, Munitions Directorate, Dept. of Industrial and Systems Engineering, University of Florida, Gainesville, USA;(4) Center for Applied Optimization, Dept. of Industrial and Systems Engineering, University of Florida, Gainesville, USA;(5) Dept. of Management Science and Engineering, Electrical Engineering, Stanford University, Stanford, USA; |
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| Abstract: | This paper studies the relationship between the so-called bi-quadratic optimization problem and its semidefinite programming (SDP) relaxation. It is shown that each r-bound approximation solution of the relaxed bi-linear SDP can be used to generate in randomized polynomial time an O(r){mathcal{O}(r)}-approximation solution of the original bi-quadratic optimization problem, where the constant in O(r){mathcal{O}(r)} does not involve the dimension of variables and the data of problems. For special cases of maximization model, we provide an approximation algorithm for the considered problems. |
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