how to write this constraint in fmincon

Hi, does any one know how to write this constraint in fmincon?

sum(abs(x- w0) ) <= 0.3

w0 is known and it is a Nx1 vevctor. x is the unkown.

Thanks in advance.

Answer 1

[Walter Roberson]

abs() can only be handled as a nonlinear constraint

function [c, ceq] = nonl(x, w0)n
c = sum(abs(x-w0)) - 0.3;
ceq = [];

And the corresponding location in the fmincon parameter list would be

@(x) nonl(x, w0)

Answer 2

[Matt J]

Because the constraint is non-smooth, you cannot use fmincon's nonlinear constraint support to implement this. Instead you have to use a more indirect method, which reformulates the problem in terms of two unknown vectors x and y. If your original problem is,

then the reformulated problem is as below (which requires only linear constraints).

[Lingjuan Ma]

Thank you both. c = sum(abs(x-w0)) - 0.3; does not always give an answer/ converge. Perhaps it is because teh constraitn is non-smooth.

[Matt J]

That's why I recommended that you don't do it! But I guess you got it to work somehow, since you ended up accepting Walter's answer?

[Lingjuan Ma]

Hi Matt, I have other constraints and Walter's answer coincided with what I had initially. But then I realised, from your answer, why sometimes it did not work. Thanks again.