Converting a Mixed SUBSET-SUM Problem To All-Positive Case


Let’s say we have a SUBSET-SUM problem with list {$ x_1,x_2,x_3,…x_N$ } and weight $ W$ , with some of $ x_i<0$ . Is there a known way, in polynomial time, to convert this problem into an equivalent problem, but with all $ x_i \geq 0$ ? And if there aren’t any, is it possible for there to be such an algorithm?