2019/02/23 by Moslem Zamani, Zamani, Moslem
Computer Science · Immunology and Microbiology · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Phagocytosis and Immune Regulation
paper · pdf · doi:10.48550/arxiv.1902.08861
openalex publication_date 2019/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs. We propose two types of bounds for quadratically constrained quadratic programs, quadratic and cubic bounds. For quadratic bounds, we use affine functions as Lagrange multipliers. We demonstrate that most semi-definite relaxations can be obtained as the dual of a quadratic bound. In addition, we study bounds obtained by changing the ground set. For cubic bounds, in addition to affine multipliers we employ quadratic functions. We provide a comparison between the proposed cubic bound and typical bounds for standard quadratic programs. Moreover, we report comparison results of a quadratic and a cubic bound for some non-convex quadratically constrained quadratic programs.