Optimization Theory

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

  1. D. Bertsekas, "Nonlinear Programming: 2nd Edition" published by Athena Scientific, 1999. (fmin, fminunc in Matlab)
  2. D. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods," Academic Press, 1982; republished by Athena Scientific, 1996.

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

  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.

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.

Convex programming

  1. S. Boyd and L. Vandenberghe, "Convex optimization".

Semidefinite programming (robust solutions to decision problems involving uncertainty)

  1. A. Ben-Tal, L. El Ghaoui, and A. Nemirovskii, "Robust Semidefinite Programming," In R. Saigal, L. Vandenberghe, H. Wolkowicz, editors, Handbook of Semidefinite Programming. Kluwer Academic Publishers, Waterloo, Canada. To appear in Spring 2000.

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.

Riemannian optimization

  1. Optimization and Dynamical Systems - Helmke and Moore. 1994, Springer-Verlag.
  2. Optimization Algorithms on Matrix Manifolds - Absil, Mahony and Sepulchre. Princeton Press, 2008.
  3. Convex functions and optimization methods on Riemannian manifolds - C. Udriste. Kluwer Academic Publishers, 1994.

     

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