With a non convex nonlinear optimization problem, would specifying the objective function as a sum of absolutes, rather than a sum of differences, make the optimization problem (significantly) more complex?

With my problem, i think working with absolutes rather than sum of squares would be better, if this does not imply a more complex optimization problem

Min X = sum(abs(x1-y1) + abs(x2-y2) + abs(x3-y3)...)

Vs

Min X = sum((x1-y1)^2 + (x2-y2)^2 + (x3-y3)^2...)

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