A Relaxed and Bound Algorithm Based on Auxiliary Variables for Quadratically Constrained Quadratic Programming Problem

Chenyang Hu, Yuelin Gao, Fuping Tian and Suxia Ma
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Chenyang Hu: School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China
Yuelin Gao: Ningxia Province Cooperative Innovation Center of Scientific Computing and Intelligent Information Processing, North Minzu University, Yinchuan 750021, China
Fuping Tian: School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China
Suxia Ma: School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021, China

Mathematics, 2022, vol. 10, issue 2, 1-18

Abstract: Quadratically constrained quadratic programs (QCQP), which often appear in engineering practice and management science, and other fields, are investigated in this paper. By introducing appropriate auxiliary variables, QCQP can be transformed into its equivalent problem (EP) with non-linear equality constraints. After these equality constraints are relaxed, a series of linear relaxation subproblems with auxiliary variables and bound constraints are generated, which can determine the effective lower bound of the global optimal value of QCQP. To enhance the compactness of sub-rectangles and improve the ability to remove sub-rectangles, two rectangle-reduction strategies are employed. Besides, two ϵ -subproblem deletion rules are introduced to improve the convergence speed of the algorithm. Therefore, a relaxation and bound algorithm based on auxiliary variables are proposed to solve QCQP. Numerical experiments show that this algorithm is effective and feasible.

Keywords: global optimization; quadratically constrained quadratic program; branch and bound method; relaxation technique (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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