Background: Environmental Engineer who works with stochastic simulation and adjacent to optimization.
As you read from my background, I work with stochastic simulation. More specifically, I work with the generation of flow scenarios from autoregressive models. The result of the simulation process is fed into a chain of optimization models that use every from linear programming to stochastic dynamic programming to mixed-integer programming to find the optimal allocation of resources.
I aspire to get closer to optimization so I can expand the topics I can work with, but I lack the background for it. I’ve been asking colleagues about ways they think I should start exposing myself to the field and the answers varied. One said I should go with Linear Programming (LP) because “it’s the basis upon which you build more advanced knowledge”. Another said I should start with Non-linear Programming (NLP) because “LP is nothing but a particular case of NLP. Once you learn NLP, you know LP”. Yet a third one said I should start with neither, instead, I should go with a general introduction to optimization (OPT) like the class notes from R. T. Rockafeller you can see here.
I know myself around Linear Algebra (LA) and Statistics & Probably (S&P). Although, I admit, I do go looking for explanations on textbooks more often than I like. I wish I knew more, and I’m watching online courses to handle this situation. (In case anyone cares to know, for LA I’m watching the video lectures from Dr. Strang from MIT made available thru MIT OCW. For S&P, I’m going with Harvard’s Statistics 101 course.).
Now, my question(s): Have you done something similar? Have you gone into optimization even though your original field didn’t prepare you for this? If so, how did you go about it? Do you know of video lectures online that were helpful to you?
I am doing my M.Sc. now and I’m certainly going to do some stochastic simulation in it and the result, as expected, will feed optimization models. I will work for a year or two more (I already have worked 4 years at this job) and then I’ll try to apply to a Ph.D. in Operations Research. While some schools are very hands-on with their OP research, some like University of Washington, CMU, Cornell, or Northwestern University are very math-y. With that said, should I learn Analysis? I have found a series of online lectures and they have both “Introduction to Analysis” course and its sequence, “Real Analysis”.
In case you have gone to a school whose OP research was math-y, how much of Real Analysis did you use? Is it a reality that you have to go in knowing it, or you can learn it while you’re there? In this topic, which deviates from the original question about how to have a foray into OPT, I’m looking for insights from those who’ve gone to strong schools/departments and how you fared.
Thank you so very much for your time and input. Your answer is highly appreciated. =)