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Any idea how we could find the w in the attached case?

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Q5 St.jpg

Problem 5: Consider the linear regression model:
t = Xw+e,
where t is an n x 1 vector and X is an n x p matrix. The fused Lasso estimates w by minimizing
the following objective function:
J(w) = [t - Xw |2+>1 /|w /1+xz> |wj+1 -wil.
where , and 2 are two positive constants. Now, consider the special case where p = 2 and
X'X = I. Find the fused Lasso estimate of w for this special case.

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