L1 minimisation for a specific function

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shaon0 2013-6-5

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https://ww2.mathworks.cn/matlabcentral/answers/78086-l1-minimisation-for-a-specific-function

Hi, I'm trying to code up the following linear program:

min norm(f(x)-d,1)

So essentially, I'm just trying to minimise the 1-norm of a function, f(x) minus the actual data, y. I've seen online that this problem can be reduced to:

min sum(i=1 to n) g(x[i]) s.t g(x[i])>=f(x[i])-d[i] and -g(x[i])>=f(x[i])-d[i]

So it reduces to a linear program. I'm very new to matlab and I know how to write out the function f(x), I can load the data d vector. But I'm not sure how I would be able to write the linear program in matlab.

Is there a sample code that anyone could provide?

Thank you in advanced.

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Matt J 2013-6-5

编辑：Matt J 2013-6-5

The reformulation you show is the right idea, but I don't know why you would have g(x[i]). I think you would just have new variables g(i) independent of x and you would minimize over the combined parameter vector [x;g]. Also, it's not a linear program unless f(x) is linear, because otherwise the constraints are still nonlinear with respect to x. Are you saying that your f(x) is linear?

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