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I'm going to assume that you optimize over the locations $x_i$. Then this is most easily reformulated via slack variables as follows: $$ \min_{x_i,s_i} s_i^2 \\ \text{so that}\quad s_i \le g(x_i) \\ \qquad\quad s_i \le 0 $$ This is not a convex problem because the feasible region described by these constraints is not convex. You can see this by just ...


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