Something doesn’t make sense here. First of all, sum(x(x<=0)) is the same as sum(min(x,0)). But that is a concave expression so the DCP rules forbid it from the left-hand side of a <= constraint.

Sorry, I have made a mistake, I want sum(abs(x(x<=0)))<=0, so it is not trivial. It is an example from Boyd and Vandenberghe book Additional Exercises for Convex Optimization, so it should work somehow. Thank you for your help, mcg.

Sorry, I have made a mistake, I want sum(abs(x(x<=0)))<=0.5, so it is not trivial. It is an example from Boyd and Vandenberghe book Additional Exercises for Convex Optimization, so it should work somehow. Thank you for your help, mcg.