New bounds for nonconvex quadratically constrained quadratic programming

Moslem Zamani*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs (QCQPs). We propose two types of bounds for QCQPs, quadratic and cubic bounds. We use affine functions as Lagrange multipliers for quadratic bounds. We demonstrate that most semidefinite 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 some quadratic and cubic bounds.
Original languageEnglish
Pages (from-to)595-613
JournalJournal of Global Optimization
Publication statusPublished - Mar 2023


  • Quadratically constrained quadratic programming
  • Reformulation-linearization technique
  • Semidefinite relaxation


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