Journal of Global Optimization

, Volume 70, Issue 1, pp 171–187 | Cite as

Argument division based branch-and-bound algorithm for unit-modulus constrained complex quadratic programming

  • Cheng Lu
  • Zhibin Deng
  • Wei-Qiang Zhang
  • Shu-Cherng Fang


This paper proposes a branch-and-bound algorithm for solving the unit-modulus constrained complex quadratic programming problems (CQPP). We study the convex hull of a unit-modulus complex variable with argument constraints, derive new valid linear inequalities from the convex hull, construct an improved semidefinite relaxation of CQPP, and then design an efficient algorithm for solving CQPP globally. The proposed algorithm branches on the sets of argument constraints and derives new valid inequalities from the partitioned sets of arguments. Numerical results are included to support the effectiveness of the proposed algorithm for finding a global solution to CQPP.


Quadratic programming Semidefinite relaxation Branch-and-bound Global optimization 


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Economics and ManagementNorth China Electric Power UniversityBeijingChina
  2. 2.School of Economics and Management, University of Chinese Academy of Sciences, Key Laboratory of Big Data Mining and Knowledge ManagementChinese Academy of SciencesBeijingChina
  3. 3.Department of Electronic EngineeringTsinghua UniversityBeijingChina
  4. 4.Department of Industrial and Systems EngineeringNorth Carolina State UniversityRaleighUSA

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