Talk:Parametric programming

	This article was reviewed by member(s) of WikiProject Articles for creation. The project works to allow users to contribute quality articles and media files to the encyclopedia and track their progress as they are developed. To participate, please visit the project page for more information.Articles for creationWikipedia:WikiProject Articles for creationTemplate:WikiProject Articles for creationAfC articles
	This article was accepted on 4 February 2015 by reviewer Jamietw (talk · contribs).

Mathematics Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

So what is big Theta?

Is the $\subset$ in $\theta \in \Theta \subset R^{m}$ strict? I.e., is the parameter space always (or usually) constrained in some way apart from the constraints $g$ ? Or can I safely change that to a $\subseteq$ for clarity? QVVERTYVS (hm?) 21:22, 4 February 2015 (UTC)[reply]

Yes indeed, the $\subset$ is strict. The reasoning behind it is the boundedness of the parameter space. If you have an unbounded space, then you would need to prove that nowhere in this unbounded space there is at least one point where another set of constraints is active (which denotes a different solution). While you might be able to construct a very simple example (say 1 parameter, 1 constraint), where you can exhaustively enumerate all the options and make this statement, in general $\subset$ has to hold. In particular when you look at nonlinear systems (see the citation to Fiacco's sensitivity theorem for that), then you see that the results only hold in a neighborhood of the initial solution point. So, to summarize: you might find some small examples where you could say $\subseteq$ , but to include this in the general problem formulation is in my opinion misleading. What do you think?