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I'm working on a non linear optimisation problem in xpress. To be able to run in in xpress it has to be a linear equation.

The equation is $x \sin x$.

The restrictions: $x < 2 \pi$

$x > 0$

I thought about using Taylor series to find an approximation for the equation, nevertheless the Taylor series is not linear. Any ideas?

Asaf Karagila
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Jose
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  • Please use formatting so that posts become more readable – Shailesh Oct 19 '15 at 01:48
  • @Shailesh Jose's new, so we should cut him some slack. – Robert Soupe Oct 19 '15 at 01:56
  • @RobertSoupe of course ; it was a gentle nudge. – Shailesh Oct 19 '15 at 02:01
  • Assuming that by linear you mean affine, you're essentially asking is to approximate $\sin x$ by some function of the form $\frac{a}{x} + b$ over $(0,2\pi)$. You can try to optimise over the constants, but this is likely to be a very bad fit. Does your system allow piecewise continuous affine objectives? In this case, you can divide $(0,2\pi)$ into a large number of segments $ \cup (x_k, x_{k+1})$, and approximate $\sin x \approx \sin x_k +c_k x$ over the intervals. – stochasticboy321 Oct 19 '15 at 02:01
  • Of course, if you simply want to maximise $x \sin x$, there are simple analytic ways to go about that. – stochasticboy321 Oct 19 '15 at 02:02
  • To begin with, $x \sin x$ is not an equation, it is just a term. How does it enter the model? In the objective? In a constraint? Etc. – Johan Löfberg Oct 20 '15 at 13:16

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