Constraining a single element in non-negative least squares

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Muhammad Haziq Kamarul Azman
Hello,
I'm using non-negative least squares to find a solution to a classic multi-parameter linear regression problem.
xhat = arg min J(x) = | | E x - f | |, subject to x >= 0,
with E a n-by-m matrix of rank m.
In one instance, I got what I needed using lsqnonneg. I then modify the problem as follows
xhat = arg min J(x) = | | Etilda x - ftilda | |, subject to x(m+1) >= 0 (i.e. only the last element of x is constrained),
with Etilda = [E etilda], etilda an n-vector. For the sake of simplicity, etilda is orthogonal to the column space of E (i.e. etilda is linearly independent of ej, the column vectors of E, j = [1:m]).
Is it possible to perform this optimization using lsqnonneg? If not, are there alternatives to that?

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