An introduction to convex optimization for communications and signal processing

Zhi Quan Luo, Wei Yu

Research output: Contribution to journalArticlepeer-review

342 Scopus citations


Convex optimization methods are widely used in the design and analysis of communication systems and signal processing algorithms. This tutorial surveys some of recent progress in this area. The tutorial contains two parts. The first part gives a survey of basic concepts and main techniques in convex optimization. Special emphasis is placed on a class of conic optimization problems, including second-order cone programming and semidefinite programming. The second half of the survey gives several examples of the application of conic programming to communication problems. We give an interpretation of Lagrangian duality in a multiuser multi-antenna communication problem; we illustrate the role of semidefinite relaxation in multiuser detection problems; we review methods to formulate robust optimization problems via second-order cone programming techniques.

Original languageEnglish (US)
Article number1664998
Pages (from-to)1426-1438
Number of pages13
JournalIEEE Journal on Selected Areas in Communications
Issue number8
StatePublished - Aug 2006

Bibliographical note

Funding Information:
Manuscript received May 3, 2006; revised May 8, 2006. The work of Z.-Q. Luo was supported in part by the National Science Foundation under Grant DMS-0312416. The work of W. Yu was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and in part by the Canada Research Chairs Program.


  • Convex optimization
  • Digital communications
  • Duality
  • Second-order cone programming (SOCP)
  • Semideflnite programming (SDP)
  • Signal processing

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