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Why not just do: $$max \,\, \mu ^T w - \lambda w^T \Sigma w$$ s.t.: $$w \leq V$$ $$-w \leq V$$ $$A w = 0$$ Google for LP absolute value constraint transformations. Here is a helpful online tutorial. And if these are portfolio weights, don't forget that they should add up to 1.
One standard approach is to shrink your forecasts towards zero (or to some reasonable value as in the Black-Littermann model). Shrinking towards zero is done by: $$w^*=\underset{w}{\text{argmax}} \ \ \lambda_{\alpha} r^Tw - \lambda_r w^{T} \Sigma w - tradingCost(|w-w_0|)\\$$ $$0\leq\lambda_{\alpha}\leq1$$ Shrinkage coefficient $\lambda_{\alpha}$ is best ...