Linear programming

  1. Bertsimas, D. and Tsitsiklis, J.: Introduction to Linear Optimization. Athena Scientific, 1997. Graduate-level text on linear programming, network flows, and discrete optimization. 
  2. Dantzig, G. B.: Linear Programming and Extensions, Princeton University Press, 1963. The most widely cited early textbook in the field.
  3. Dantzig, George B. and Thapa, Mukund N.: Linear Programming 1: Introduction, Springer Verlag, 1997. 
  4. Luenberger, D. G.: Introduction to Linear and Nonlinear Programming, Addison Wesley, 1984. Updated version of an old classic. Well suited for beginners. 
  5. Nash, S. and Sofer, A.: Linear and Nonlinear Programming, McGraw-Hill, 1996. 
  6. Roos, C., Terlaky T. and Vial, J. Ph.: Theory and Algorithms for Linear Optimization: An Interior Point Approach. John Wiley, Chichester, 1997. 
  7. Schrijver, A.: Theory of Linear and Integer Programming, John Wiley, 1988. Advanced, very well written. 
  8. Vanderbei, R. J.: Linear Programming: Foundations and Extensions. Kluwer Academic Publishers, 1996. Balanced coverage of simplex and interior-point methods. Source code available on-line for all algorithms presented. 
  9. Williams, H.P., Model Building in Mathematical Programming, John Wiley 1999, 4th edition. Little on algorithms, but excellent for learning what makes a good model. 
  10. Wright, St. J.: Primal-Dual Interior-Point Methods. SIAM Publications, 1997. Covers theoretical, practical and computational aspects of the most important and useful class of interior-point algorithms. 
  11. Ye, Yinyu: Interior Point Algorithms: Theory and Analysis. John Wiley, 1997. 

Nonlinear programming

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  1. D. Bertsekas, "Nonlinear Programming: 2nd Edition" published by Athena Scientific, 1999. (fmin, fminunc, fmincon in Matlab)
  2. D. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods," Academic Press, 1982; republished by Athena Scientific, 1996.
  3. S. Boyd and L. Vandenberghe, "Convex optimization".
  4. David G. Luenberger, ``Optimization by vector space methods,'' New York: Wiley, 1969.
  5. R. Reemtsen and Jan J. R. Uckmann, ``Semi-Infinite Programming,'' Kluwer Academic Publishers, 1998.

Network programming

  1. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, "Network flows: Theory, Algorithms, and Applications," Prentice-Hall, Englewood Cliffs, N. J., 1993.
  2. D. Bertsekas, "Network Optimization: Continuous and Discrete Models," Athena Scientific, 1998.

Integer programming

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  1. G. L. Nemhauser and L. A. Wolsey, "Integer and Combinatorial Optimization," John Wiley & Sons, New York, 1988.
  2. C. H. Papadimitriou and K. Steiglitz, "Combinatorial Optimization: Algorithm and Complexity," Prentice Hall, Englewood Cliffs, N. J., 1982.
  3. L. A. Wolsey, "Integer Programming," John Wiley & Sons, New York, 1998.
  4. Bernhard Korte, Jens Vygen, ``Combinatorial optimization : theory and algorithms,'' Berlin; New York: Springer, 2000.

Stochastic programming & Dynamic programming

  1. D. Bertsekas, "Dynamic Programming and Optimal Control Vol. 1: 2nd Edition," Athena Scientific, 2000.
  2. D. Bertsekas, "Dynamic Programming and Optimal Control Vol. 1, 2," Athena Scientific, 1995.
  3. D. Bertsekas and J. Tsitsiklis, "Neuro-Dynamic Programming," Athena Scientific, 1996.
  4. D. Bertsekas and S. E. Shreve, "Stochastic Optimal Control: The Discrete-Time Case," Athena Scientific, 1996.
  5. D. Bertsekas, "Dynamic Programming: Deterministic and Stochastic Models," Prentice-Hall, 1987.
  6. P. Kall and S. W. Wallace, "Stochastic Programming," John Wiley & Sons, New York, 1994.
  7. J. R. Birge and F. Louveaux, "Introduction to Stochastic Programming," Springer-Verlag, New York, 1997.
  8. L. I. Sennott, "Stochastic Dynamic Programming and the Control of Queueing Systems," John Wiley & Sons, 1999.
  9. M. L. Puterman, "Markov Decision Processes: Discrete Stochastic Dynamic Programming," John Wiley & Sons, 1994.

Semidefinite programming (robust solutions to decision problems involving uncertainty)

  1. Henry Wolkowicz, Romesh Saigal, Lieven Vandenberghe (ed.), ``Handbook of semidefinite programming : theory, algorithms, and applications,'' Boston : Kluwer Academic, c2000. 

Nonsmooth optimization

  1. M. R. Osborne, "Finite Algorithms in Optimization and Data Analysis," John Wiley & Sons, 1985.
  2. R. Fletcher, "Practical Methods of Optimization," 2nd Ed., John Wiley & Sons, New York, 1987.
  3. J.-B. Hiriart-Urruty and C. Lemarechal, "Convex Analysis and Minimization Algorithms," Springer-Verlag, 1993.

Numerical optimization

  1. J. Nocedal and S. J. Wright, "Numerical Optimization," Springer, 1999.
  2. D. Bertsekas, "Parallel and Distributed Computation: Numerical Methods," Prentice-Hall, 1989; republished by Athena Scientific, 1997.

Multi-objective optimization

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  1. Kalyanmoy Deb, "Multi-objective optimization using evolutionary algorithms," Chichester ; New York : John Wiley & Sons, c2001.
  2. P. Seratini, (Editor) ``Mathematics of Multi Objective Optimization,'' Springer Verlag, March 1986.
  3. Ralph Steuer, ``Multiple Criteria Optimization: Theory, Computation, and Application,'' Krieger Publishing Company, January 1986.
  4. Matthias Ehrgott (Editor), Xavier Gandibleux (Editor), ``Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys,'' Kluwer Academic Publishers; ISBN: 1402071280; (June 2002).
  5. Evangelos Triantaphyllou, ``Multi-Criteria Decision Making Methods: A comparative Study,'' Kluwer Academic Publishers; ISBN: 0792366077; (November 2000)
  6. G. P. Liu, Jian-Bo Yang, J. F. Whidborne, ``Multiobjective Optimisation & Control,'' Taylor & Francis; ISBN: 0863802648; 1st edition (June 15, 2002)
  7. Y. Sawaragi, H. Nakayama, and T. Tanino, Theory of Multi-objective Optimization. Orlando:Academic Press, 1985.
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