|Originally posted by trancaholic |
Well, I *made* that part of the problem linear.
Basically, the work could be generalized to yield constraints of any kind, at a cost of more complex notation in the resulting article. As to how that part of the problem was solved: It was a "proof of concept"-implementation to support my paper, so I simply got hold of a Java package that could do that part for me. Of course, getting to know the quirks of the API of the package I got hold of, and making it work with another general purpose linear algebra package and my own classes, turned out to be much more time consuming than had I written the entire thing from scratch myself.
The only thing I did that was remotely interesting from your point of view, was to invent a simple method for eliminating redundant constraints from my set of constraints, as that set was built. It was polynomial in the number of constraints already in the set and exponential in the dimensionality of the constraints. That suited me ok, as the number of constraints were always >>100 and the number of dimensions were <4 in nearly all cases.
Anyway, I did cry out for help quite a few times on specifics on mathematical programming, and apart from some professor who wanted me to buy his book, I didn't get much feedback from usenet. Next time I'll jump at you instead.
Very interesting. I do the opposite: Start spending a lot of time here, and then cool my brain off by drinking beer with my office mate instead of doing research. Come to think of it, you're probably better off with your arrangement.
Ignoring Dupz's post (), I have to ask whether your "proof of concept" was a feasibility or an optimization problem. As for making it linear, you did well. Everything else is much tougher to solve. I'm guessing that the JAVA package you used implemented the Simplex algorithm to solve the problem, although there are tons of pre-solvers out there (open source) that you could have used to remove redundant constraints before solving it, thus sparing you the trouble to create one. And yeah, definitely don't hesitate to ask for help As for my arrangement, I prefer yours