References

If a single reference book on nonlinear optimization is to be recommended, be it [1] that sits on your bookshelf.

If one or two more can still fit, [2], [3] are classical comprehensive references on nonlinear programming (the latter covers linear programming too).

While all the three books are true classics, they are only available for purchase. Fortunately, there is a wealth of resources that are freely available online such as the notes [4] accompanying a course on optimal control, which do a decent job of introduction to a nonlinear programming, and beautifully typeset modern textbooks [5] and [6]. The former is even based on Julia language, while the latter has also its online html version. Yet another high-quality textbook that is freely available online is [7].

When restricting to convex optimization, the bible of this field [8] is also freely available online. It is a must-have for everyone interested in optimization. Yet another advanced treatment of convex optimization is [9], which is also freely available online.

Maybe a bit unexpected resources on the optimization theory are materials accompanying some optimization software. Particularly recommendable is [10], it is very useful even if you do not intend to use their software. In particular, their introduction to conic optimization is very well written and easy to follow.

Some practical aspects are discussed in Guidelines for Numerical Issues for Gurobi Optimizer.

References

[1]

J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. in Springer Series in Operations Research and Financial Engineering. New York: Springer, 2006. Available: https://doi.org/10.1007/978-0-387-40065-5

[2]

D. Bertsekas, Nonlinear Programming, 3rd ed. Belmont, Mass: Athena Scientific, 2016. Available: http://www.athenasc.com/nonlinbook.html

[3]

D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 5th ed. in International Series in Operations Research & Management Science, no. 228. Cham, Switzerland: Springer, 2021. Available: https://doi.org/10.1007/978-3-030-85450-8

[4]

S. Gros and M. Diehl, “Numerical Optimal Control (Draft).” Systems Control; Optimization Laboratory IMTEK, Faculty of Engineering, University of Freiburg, Apr. 2022. Available: https://www.syscop.de/files/2020ss/NOC/book-NOCSE.pdf

[5]

M. J. Kochenderfer and T. A. Wheeler, Algorithms for Optimization. The MIT Press, 2019. Accessed: Dec. 29, 2020. [Online]. Available: https://algorithmsbook.com/optimization/

[6]

J. R. R. A. Martins and A. Ning, Engineering Design Optimization. Cambridge ; New York, NY: Cambridge University Press, 2022. Available: https://mdobook.github.io/

[7]

M. Bierlaire, Optimization: Principles and Algorithms, 2nd ed. Lausanne: EPFL Press, 2018. Available: https://transp-or.epfl.ch/books/optimization/html/OptimizationPrinciplesAlgorithms2018.pdf

[8]

S. Boyd and L. Vandenberghe, Convex Optimization, Seventh printing with corrections 2009. Cambridge, UK: Cambridge University Press, 2004. Available: https://web.stanford.edu/~boyd/cvxbook/

[9]

A. Ben-Tal and A. Nemirovski, “Lectures on Modern Convex Optimization - 2020/2021/2022/2023 Analysis, Algorithms, Engineering Applications,” Technion & Georgia Institute of Technology, 2023. Available: https://www2.isye.gatech.edu/~nemirovs/LMCOLN2023Spring.pdf

[10]

“MOSEK Modeling Cookbook.” Mosek ApS, Sep. 2024. Available: https://docs.mosek.com/MOSEKModelingCookbook-a4paper.pdf