Wikipedia:Reference desk/Archives/Mathematics/2016 June 25

= June 25 =

Variation on Qudratic Programming
Is the following problem NP-complete? $$L=\{ | Q\ is\ n\times n\ matrix,\ ,\lambda\in\R,\ \exists x ( x^T Qx<\lambda,\ \exists i( x_i\in [0,1], \forall j\ne i \ x_j\in\{0,1\})) \} $$ עברית (talk) 07:53, 25 June 2016 (UTC)


 * There is always a solution: set all x's equal to 0. Loraof (talk) 15:02, 25 June 2016 (UTC) That's assuming lambda is positive. Loraof (talk) 15:04, 25 June 2016 (UTC)
 * After thinking about it for a while, it seems NP-hard to me, but I can't find a proof of that. Loraof (talk) 19:49, 25 June 2016 (UTC)


 * I don't assume that $$\lambda$$ is positive. (nor I assume Q's entries to be positive) 132.67.104.216 (talk) 15:24, 26 June 2016 (UTC)
 * I'm not an expert but AFAIK questions of computability and complexity are usually asked about countable sets. The inputs and witnesses are based on integers. I think you have wholly different questions when you put real numbers in the mix. A classical Turing machine can't operate on real numbers.
 * That said, I think the problem will not materially change if you replace all occurrences of real numbers with rational numbers, and then I think they can be handled safely. -- Meni Rosenfeld (talk) 10:49, 27 June 2016 (UTC)