Optimization Theory

Linear programming
- Bertsimas, D. and Tsitsiklis, J.: Introduction to Linear Optimization. Athena Scientific, 1997. Graduate-level text on linear programming, network flows, and
discrete optimization.
- Dantzig, G. B.: Linear Programming and Extensions, Princeton University Press, 1963. The most widely cited early textbook in the field.
- Dantzig, George B. and Thapa, Mukund N.: Linear Programming 1: Introduction, Springer Verlag, 1997.
- Luenberger, D. G.: Introduction to Linear and Nonlinear Programming, Addison Wesley, 1984. Updated version of an old classic. Well suited for
beginners.
- Nash, S. and Sofer, A.: Linear and Nonlinear Programming, McGraw-Hill, 1996.
- Roos, C., Terlaky T. and Vial, J. Ph.: Theory and Algorithms for Linear Optimization: An Interior Point Approach. John Wiley, Chichester, 1997.
- Schrijver, A.: Theory of Linear and Integer Programming, John Wiley, 1988. Advanced, very well written.
- 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.
- 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.
- 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.
- Ye, Yinyu: Interior Point Algorithms: Theory and Analysis. John Wiley, 1997.
Nonlinear programming
- D. Bertsekas, "Nonlinear Programming: 2nd Edition" published by Athena Scientific, 1999.
(fmin, fminunc in Matlab)
- D. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods," Academic Press, 1982; republished by Athena Scientific, 1996.
Network programming
- R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, "Network flows: Theory,
Algorithms, and Applications," Prentice-Hall, Englewood Cliffs, N. J.,
1993.
- D. Bertsekas, "Network Optimization: Continuous and Discrete Models," Athena Scientific, 1998.
Integer programming
- G. L. Nemhauser and L. A. Wolsey, "Integer and Combinatorial
Optimization," John Wiley & Sons, New York, 1988.
- C. H. Papadimitriou and K. Steiglitz, "Combinatorial Optimization:
Algorithm and Complexity," Prentice Hall, Englewood Cliffs, N. J.,
1982.
- L. A. Wolsey, "Integer Programming," John Wiley & Sons, New
York, 1998.
Stochastic programming & Dynamic programming
- D. Bertsekas, "Dynamic Programming and Optimal Control Vol. 1: 2nd Edition," Athena Scientific, 2000.
- D. Bertsekas, "Dynamic Programming and Optimal Control Vol. 1, 2," Athena Scientific, 1995.
- D. Bertsekas and J. Tsitsiklis, "Neuro-Dynamic Programming," Athena Scientific, 1996.
- D. Bertsekas and S. E. Shreve, "Stochastic Optimal Control: The Discrete-Time Case," Athena Scientific, 1996.
- D. Bertsekas, "Dynamic Programming: Deterministic and Stochastic Models," Prentice-Hall,
1987.
- P. Kall and S. W. Wallace, "Stochastic Programming," John Wiley
& Sons, New York, 1994.
- J. R. Birge and F. Louveaux, "Introduction to Stochastic
Programming," Springer-Verlag, New York, 1997.
- L. I. Sennott, "Stochastic Dynamic Programming and the Control of
Queueing Systems," John Wiley & Sons, 1999.
- M. L. Puterman, "Markov Decision Processes: Discrete Stochastic
Dynamic Programming," John Wiley & Sons, 1994.
Convex programming
- S. Boyd and L. Vandenberghe, "Convex optimization".
Semidefinite programming (robust solutions to decision problems involving uncertainty)
- 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
- M. R. Osborne, "Finite Algorithms in Optimization and Data
Analysis," John Wiley & Sons, 1985.
- R. Fletcher, "Practical Methods of Optimization," 2nd Ed., John
Wiley & Sons, New York, 1987.
- J.-B. Hiriart-Urruty and C. Lemarechal, "Convex Analysis and
Minimization Algorithms," Springer-Verlag, 1993.
Numerical optimization
- J. Nocedal and S. J. Wright, "Numerical Optimization," Springer,
1999.
- D. Bertsekas, "Parallel and Distributed Computation: Numerical Methods," Prentice-Hall, 1989; republished by Athena Scientific, 1997.
Riemannian optimization
- Optimization and Dynamical Systems -
Helmke and
Moore. 1994,
Springer-Verlag.
-
Optimization Algorithms on Matrix Manifolds -
Absil,
Mahony and
Sepulchre.
Princeton Press, 2008.
- Convex functions and optimization methods on Riemannian manifolds - C.
Udriste. Kluwer Academic Publishers, 1994.
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