# Can this problem be written as a linear program?

 0 I have this objective function: $$\text{minimize} \quad \frac{\sum^n_{i=1} {c_i x_i}}{1 - \sum^n_{i=1} c_i x_i} + \sum^n_{i=1} t_i c_i x_i$$ subject to: $$\sum^n_{i=1} {c_i x_i} \leq 1$$ $$0 \le x \le 1$$ where $$r$$ and $$c$$ are continuous given vectors. Is it possible to convert it into a linear program? Thank you. asked 28 Sep '17, 08:27 ftam 11●2 accept rate: 0% fbahr ♦ 4.6k●7●16 Is this a homework problem? (28 Sep '17, 09:52) Mark L Stone Mark L Stone, No, it is a model for solving a trading problem with nonlinear optimization, but it took too long for large problems. do you have a suggestion? (28 Sep '17, 09:56) ftam 1 https://en.wikipedia.org/wiki/Linear-fractional_programming (28 Sep '17, 10:03) Mark L Stone Thank you Mark, my problem is how to deal with the second term if I reformulate it as a linear fractional program? (28 Sep '17, 10:07) ftam I leave that for you an an exercise to work out, including whether it can be. (28 Sep '17, 10:10) Mark L Stone 2 Mark, you need to start putting your answers in answer blocks, rather than comments, so that you can accumulate karma credits. They might be useful after the impending apocalypse. (28 Sep '17, 16:28) Paul Rubin ♦♦ How strong is OR Exchange's cyber security? Even if I acquire a large number of karma points, it will all be for naught if Russia, China, Iran, or North Korea hack the site, reducing the USD value of the cache from zip to zilch. (28 Sep '17, 19:45) Mark L Stone 3 Based on the number of spammer accounts, I'd say our security is NP-hard (as in, "Not Particularly-hard"). (28 Sep '17, 23:11) Paul Rubin ♦♦ @Mark L Stone, So that is called a linear plus linear fractional program, it is clearly not as easy as the linear fractional programming. (13 Oct '17, 05:03) ftam showing 5 of 9 show 4 more comments
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