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I recently completed an undergraduate course in Linear Programming and Operations Research. I am willing to look into advanced concepts and Non-Linear Optimization algorithms and also, their method of implementation using a programming language/toolbox. I would be glad if I am guided towards specific resources.

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There are plenty of courses and books out there. For convex optimization I'd take a look into Boyd's & Vandenberghe's lecture which also has a good accompanying script. The lecture/book from Nemirovsky & Ben-Tal is also very good. If you are looking into algorithms that can be used for general (non-convex) problems, you might want for example look into the nonlinear programming course at MIT by Bertsekas. There are more advanced topics like optimization with differential equations or the interplay of optimization methods and machine/deep learning. But I'd start out with the more general ones before going into the more advanced ones.

As a personal note, I advise you to also look at the discrete part of OR, i.e. the Mixed-Integer Programming world which is a nice advanced topic which you could explore coming from linear programming. The interplay of mixed-integer and nonlinear problems is even more advanced (and interesting).

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    $\begingroup$ Also see references at or.stackexchange.com/questions/869/… , particularly J. Nocedal, S. Wright. "Numerical Optimization". Note my comment on Nemirovsky & Ben-Tal: "Very advanced mathematically". And why in the heck is that linked topic closed? Give me a break. $\endgroup$
    – Mark L. Stone
    Nov 25, 2019 at 2:13
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    $\begingroup$ If you want to solve convex nonlinear models consulting docs.mosek.com/modeling-cookbook/index.html might be worthwhile. $\endgroup$
    – ErlingMOSEK
    Nov 25, 2019 at 6:37
  • $\begingroup$ +1 @ErlingMOSEK . I included that on the Wiki answer at the link in my comment above. I referenced the log-sum-inv modeling solution there a couple of days ago to answer a CVX Forum question. $\endgroup$
    – Mark L. Stone
    Nov 25, 2019 at 12:45

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