Closest Vector Problem in the 1-Norm. Mixed-Integer Linear Programming Formulation

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So I understand the closest vector problem in the infinity-norm and getting to the final step of the program where I have:

Minimize z Subject to z >= xj - tj for j = 1,2,...,n z >= tj - xj for j = 1,2,...,n

Okay so how do I do the exact same thing except in the 1-Norm? Any help would be greatly appreciated!