Approximation Bounds for Trilinear and Biquadratic Optimization Problems Over Nonconvex Constraints

Yuning Yang, Qingzhi Yang, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


This paper presents new approximation bounds for trilinear and biquadratic optimization problems over nonconvex constraints. We first consider the partial semidefinite relaxation of the original problem, and show that there is a bounded approximation solution to it. This will be achieved by determining the diameters of certain convex bodies. We then show that there is also a bounded approximation solution to the original problem via extracting the approximation solution of its semidefinite relaxation. Under some conditions, the approximation bounds obtained in this paper improve those in the literature.
Original languageEnglish
Pages (from-to)841-858
Number of pages18
JournalJournal of Optimization Theory and Applications
Issue number3
Publication statusPublished - 1 Jan 2014


  • Approximation bound
  • Biquadratic optimization
  • Convex bodies
  • Semidefinite relaxation
  • Trilinear optimization

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research

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