Optimization algorithm

Hi

I want to know if it's possible to solve for the value of k and u in this optimization problem:

max Au=b
k in [0,1] % [0,1] is an interval

A = [2k 1 0;-1 2k 1;0 -1 2k]
u = [u1 u2 u3]
b = [1 0 -2]

This is a bad example because k=0 is a solution, but in general case, what type of algorithm can solve this type of problems ?

Thank's
David
.

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