Branch-and-Reduction Algorithm for Indefinite Quadratic Programming Problem. (30th March 2021)

• Record Type: Journal Article
• Authors: Qiu, Yongjian; Zhu, Yuming; Yin, Jingben
• Other Names: Lv Zhihan Academic Editor.
• Is Part Of: Complexity. Volume 2021(2021)
• Publication Date: 2021-03-30
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2021/5578427
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : This paper presents a rectangular branch-and-reduction algorithm for globally solving indefinite quadratic programming problem (IQPP), which has a wide application in engineering design and optimization. In this algorithm, first of all, we convert the IQPP into an equivalent bilinear optimization problem (EBOP). Next, a novel linearizing technique is presented for deriving the linear relaxation programs problem (LRPP) of the EBOP, which can be used to obtain the lower bound of the global optimal value to the EBOP. To obtain a global optimal solution of the EBOP, the main computational task of the proposed algorithm involves the solutions of a sequence of LRPP. Moreover, the global convergent property of the algorithm is proved, and numerical experiments demonstrate the higher computational performance of the algorithm.