References

If a single reference book on nonlinear optimization is to be recommended, be it (Nocedal and Wright 2006) that sits on your book shelf.

If one or two more can still fit, (Bertsekas 2016), (Luenberger and Ye 2021) are classical comprehensive references on nonlinear programming (the latter covers linear programming too).

While all the three books are only available for purchase, there is a wealth of resources are freely available online such as the notes (Gros and Diehl 2022) accompanying a course on optimal control, which do a decent job of introduction to a nonlinear programming, and beautifully typeset modern textbooks (Kochenderfer and Wheeler 2019) and (Martins and Ning 2022), the former based on Julia language. Yet another high-quality textbook that is freely available online is (Bierlaire 2018).

When restricting to convex optimization, the bible of this field (Boyd and Vandenberghe 2004) is also freely available online. It is a must-have for everyone interested in optimization. Another textbook biased towards convex optimization is (Calafiore 2014), which is freely accessible through its web version. Yet another advanced and treatment of convex optimization is (Ben-Tal and Nemirovski 2023), which is also freely available online.

Maybe a bit unexpected resources on theory are materials accompanying some optimization software. Partilarly recommendable is (“MOSEK Modeling Cookbook” 2024), it is very useful even if you do not indend to use their software.

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References

Ben-Tal, Aharon, and Arkadi Nemirovski. 2023. “Lectures on Modern Convex Optimization - 2020/2021/2022/2023 Analysis, Algorithms, Engineering Applications.” Lecture Notes. Technion & Georgia Institute of Technology. https://www2.isye.gatech.edu/~nemirovs/LMCOLN2023Spring.pdf.
Bertsekas, Dimitri. 2016. Nonlinear Programming. 3rd ed. Belmont, Mass: Athena Scientific. http://www.athenasc.com/nonlinbook.html.
Bierlaire, Michel. 2018. Optimization: Principles and Algorithms. 2nd ed. Lausanne: EPFL Press. https://transp-or.epfl.ch/books/optimization/html/OptimizationPrinciplesAlgorithms2018.pdf.
Boyd, Stephen, and Lieven Vandenberghe. 2004. Convex Optimization. Seventh printing with corrections 2009. Cambridge, UK: Cambridge University Press. https://web.stanford.edu/~boyd/cvxbook/.
Calafiore, Giuseppe C. 2014. Optimization Models. Cambridge, UK: Cambridge University Press. https://people.eecs.berkeley.edu/~elghaoui/optmodbook.html.
Gros, Sebastien, and Moritz Diehl. 2022. “Numerical Optimal Control (Draft).” Systems Control; Optimization Laboratory IMTEK, Faculty of Engineering, University of Freiburg. https://www.syscop.de/files/2020ss/NOC/book-NOCSE.pdf.
Kochenderfer, Mykel J., and Tim A. Wheeler. 2019. Algorithms for Optimization. The MIT Press. https://algorithmsbook.com/optimization/.
Luenberger, David G., and Yinyu Ye. 2021. Linear and Nonlinear Programming. 5th ed. Vol. 228. International Series in Operations Research & Management Science. Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-030-85450-8.
Martins, Joaquim R. R. A., and Andrew Ning. 2022. Engineering Design Optimization. Cambridge ; New York, NY: Cambridge University Press. https://mdobook.github.io/.
“MOSEK Modeling Cookbook.” 2024. Mosek ApS. https://docs.mosek.com/MOSEKModelingCookbook-a4paper.pdf.
Nocedal, Jorge, and Stephen Wright. 2006. Numerical Optimization. 2nd ed. Springer Series in Operations Research and Financial Engineering. New York: Springer. https://doi.org/10.1007/978-0-387-40065-5.