ECE 744 – Optimization for communication networks


Design of current wireless networks is increasingly faced with the challenge of guaranteeing given quality-of-service or cost constraints, while providing optimal performance in terms of resource utilization. In addition, the emerging paradigm of decentralized wireless networks, such as ad hoc and sensor networks, calls for optimization techniques to be performed in a distributed, and possibly competitive, fashion by different radio transceivers. This course covers the basic analytical and algorithmic tools that enable such centralized and decentralized optimization. Specific topics include single-objective convex optimization (duality, optimality conditions, algorithms) and fundamentals of multi-objective optimization and game theory.   


Graduate-level knowledge of linear algebra.


Dr. Osvaldo Simeone
Phone: (973) 596-5710
Office: 211 ECE Dept. 
Office Hours: Wednesday 2-6pm


[Boyd] S. Boyd and L. Vandenberghe, Convex optimization, Cambridge, 2004, ISBN 0521833787. [on-line]


Other references:



[Bert] D. P. Bertsekas, Nonlinear programming, Athena Scientic, 1999.

[Bert2]  D. P. Bertsekas, Angelia Nedic and Asuman E. Ozdaglar, Convex Analysis and optimization, Athena Scientific, 2003.

[Bert3] D. P. Bertsekas, Convex optimization theory, Athena Scientific, 2009.

[Baz] M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear programming, Wiley, 2006.

[Chong] E. K. P. Chong and S. H. Zak, An introduction to optimization, Wiley, 2001.

[Mac] A. B. MacKenzie and L. A. DaSilva, Game theory for wireless engineers, Morgan & Claypool publ., 2006.

[Tsi] D. P. Bertsekas and J. N. Tsitsiklis, Parallel and distributed computation: numerical methods, Athena scientific, 1997.

[Miet] K. M. Miettinen, Nonlinear multiobjective optimization, Kluwer, 1998.

[Osb] M. J. Osborne and A. Rubenstein, A Course in Game Theory, MIT Press, 1994.


There will one midterm (30%), and one final exam (40%) plus a project (30%).

For the project, a recent paper will be assigned to each student based on individual interests. A report written in Latex, containing MATLAB simulation results, is to be returned by the date of the final exam.

Problems will be assigned weekly but not graded.

Some links and resources:


·       Midterm Fall 2007: Solutions and grades

·       Final Fall 2007: Solutions and grades

(grade mapping after final -- 6-7: C+, 7-8: B, 8-9: B+, 9-10: A).

·       Midterm Fall 2011: Solutions

·       Final Fall 2012: Solutions

(grade mapping after final -- 6-7: C+, 7-8: B, 8-9: B+, 9-10: A).

·       Midterm Fall 2014: Text and solutions

·       Final Fall 2014: Text and solutions

Fall 2014: Tentative schedule






Sept. 2


·       Single and multi-objective, competitive optimization (game theory)

·       Convex vs. non-convex problems

Examples and applications

   Boyd – Ch. 1


    Mac – Ch. 1


Sept. 9 Sept. 16

Background and main analytical tools:

·       Convex sets

  Boyd –

       Sec. 2.1-2.5


  Bert – App. B


Sept. 23 Sept. 30

Background and main analytical tools:

·       Convex functions

 Boyd –

  Sec. 3.1, 3.2,      

    3.4.1, 3.4.2


Oct. 7

Optimization problems:

·       Definitions and optimality conditions

·       KKT conditions


Convex optimization problems

·       Main properties

 Boyd – Sec. 4.1,



 Bert – Sec. 1.1,




Oct. 14




Oct. 21

Optimality conditions for convex problems


Classes of convex problems: LP, QP, SOCP, SDP


 Boyd – Sec.

         4.2- 4.5



Oct. 28

Nov. 4

  Nov. 11

Duality theory:

·       geometric interpretation

·       the dual problem

·       duality gap

·       Constraint qualifications and KKT conditions


  Boyd – Ch. 5,

               9, 11


  Bert2 – Ch. 4-5


Nov. 18

Dec. 2

Algorithms: gradient, Newton, projected gradient


Multi-objective problems and game theory:

·       Pareto optimality

·       Non-cooperative strategic games: zero and non-zero sum, Nash equilibrium

      Miet – 2

  Mac – 3, 4, 5