We know convex quadratic programming is in $P$.
Is it also in $P$ if the function of interest is only convex in the domain of interest?
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$\begingroup$ Could you ask a more precise question? E.g., trivially speaking, if the domain of interest is not convex then the problem can be easily NP-Hard, for intance, binary QP, where the domain of interest is $\{\pm1\}$. If the domain is convex, but not easy to test membership in, even then membership in $P$ may fail .... $\endgroup$– SuvritCommented Sep 6, 2017 at 19:26
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