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I am a second year PhD student, and I still don't have an advisor. I chose this school because it has a ton of people working in the sub-field I am interested in (Mathematical Optimization). I tried lab rotations with three of the 'stars' here, but they didn't work out - two were busy during the quarter and didn't give me a problem to work on, the third one, though so far sufficiently satisfied by my work, has almost a year-long 'testing period' before taking on students, which is too long for me (I only got to know this mid-way through the last quarter).

So I relaxed my constraints and talked to professors working in a slightly different field (Control Theory), and they are willing to take me, but this means I might be doing something a bit different than what I had imagined when I came here.

Before coming to school, I was working in the industry for three years, earning a decent amount of money. I already had a Master's before that. I came back to grad school only because I wanted to work on Optimization problems and do algorithm analysis for them. Now I might have to do modeling of problems in Control Theory. The mathematics at the heart of the two fields is quite different, and I already spent a whole year taking hardcore Optimization and Convex Analysis classes (which I now feel will be a waste).

All this is making me depressed. Quitting is absolutely not an option for me.

My question is this - do people do one thing and then end up getting back on track doing what they really want to do? Is this even possible? Especially if what you really want to do is math-intensive.

EDIT, March 2017 : In case some other PhD student comes in reading this, I can imagine what you are going through with all your 'failed' rotations. Just wanted to say, I tried a rotation with a 'star' in my field of interest (Optimization) one last (fourth) time. And he has now agreed to be my advisor! :) :) :) :) :) :) :) I won't have to compromise after all, and I am so, so, so happy.

  • Quitting is absolutely not an option for me. -- What about moving? – JeffE Jan 1 '17 at 14:30
  • @JeffE I don't think I would be competitive at all against students applying to top places. I am currently in a top-20 program but no admissions committee from a higher ranked school would be impressed with my one and a half years of unfinished projects. Also, this was the best offer I had got two years ago when I first applied; if they rejected me then, my app would not be stronger now to be accepted. And also, I am 27. I already feel like I have wasted two years chasing the (so far) elusive dream of doing optimization. Applying to other schools would for sure increase the sunk cost. – user42273 Jan 1 '17 at 17:24
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    Are you sure that there is no application for the math you learned in the other subfield? I would not be so sure - I usually find that unexpected usages of mathematics/mathematical methods (i am a physicist) exist. – Sascha Jan 1 '17 at 17:39
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    As Sascha stated above, there is a large sub-field in "Control Theory" closely interconnected with "Optimization". It is called "Optimal Control" where you essentially solve optimization problems under the constraint posed by the system dynamics. Various sub-branches with significant research activity belong therein such as Model Predictive Control (MPC) (also called receding horizon control), dynamic programming, reinforcement learning etc – CTNT Jan 3 '17 at 0:16
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Let's see if your department can get its act together to do right by you. Here's what I would suggest:

  1. Write up your specific efforts to start working with a professor on a research project in your area. Keep it all very factual and neutral in tone, and keep it to one page maximum. Then make a cheat sheet (outline) that will help you present your information in a conversation. Make an appointment to speak with some department administrator, maybe you have a dean of graduate studies, for the purposes of asking for advice. Explain your problem, glancing at your cheat sheet as needed, and then leave the long version with him or her to refer to after you leave. Ask the dean when would be a good time to meet again for follow-up.

    If s/he gives you specific suggestions, try not to let your frustrations show at the beginning, and even if you know the suggestions are a waste of time, do make a good faith attempt to follow them; then report back.

If, after this, your department doesn't solve the problem, then you'll need to take some initiative.

  1. (a) Apply elsewhere. Apply to at least one "stretch" school. Even a school that is not top of the line should handle this better than your current program has been doing. Make sure that the departments you apply to have at least three people who do the right kind of work.

  2. (b) Look for a mentor to work with from a distance. Here's how you find one: read some papers, write to an author with a question about a paper you read. When you get a friendly, encouraging response from someone, then you can explain the quandary you are in and hopefully start getting some guidance.

I suggest you send some applications right away just in case. In other words, it would be wise to start with 2a because we're already in January. Then comes 1. While you are waiting for things to percolate, you can start working on #2b.

I studied math programming at UW-Madison (a long time ago). You should not have to switch streams just because your department can't get its act together.

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If you really want to do convex optimization and you are really unsure that control theory is something that would interest you, then I would strongly encourage you to

  1. continue in your project with the optimization "star" in the hopes that it will transition into an advisor/advisee relationship,
  2. research more into control theory to see if it is acceptable for you, or
  3. apply elsewhere.

Having said the above, my answers to your questions are below.

do people do one thing and then end up getting back on track doing what they really want to do?

It depends on how closely related those things happen to be.

In your case, you are really interested in convex optimization (reading over your other posts, I assume you are in EE), you have not had much luck getting anyone in the convex optimization area to take you on, but you have gotten some interest going among some potential advisors in control theory. The question is: how closely related are convex optimization and control theory?

There are two comments above that attempt to make the case that control theory and convex optimization are close enough to make it work: I happen to disagree. These two subfields of EE do not overlap in any useful way, except that they both require some mathematical maturity, which is one thing you seem to care about.

So, where do we stand?

In the best-case scenario (according to the two commenters above), your experiences in control theory will help you in your quest to eventually do what you want to do (convex optimization), and, in the worst-case scenario (my view), you will, at the very least, attain some level of much-needed mathematical maturity from control theory to maybe do convex optimization research in the future. You certainly have some things to think about going forward.

Is this even possible?

Sure. Here's one way I could see this working out for you:

After you finish your PhD, say, in control theory, you would transition to a postdoc in convex optimization. Again, taking the optimistic view of the two commenters above, you should be able to transition smoothly into a postdoc in your desired area. In my "pessimistic" opinion, I would strongly encourage you to have a side project (or three) in your target area while you are doing your PhD studies in control theory. This way, you will be able to talk with experts in convex optimization, have intelligent conversations and discuss how you can get involved in a project as a postdoc, rather than just hoping they give you a chance.

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