Is the reduce should take a place

1. At the optimal solutions only (=any optimal solution with 2 weights vectors can be represented as a solution with one weights vector such as the binary case, so solutions are equal)?

Or

2. Generally, which means that every f with 2 weight vectors can be represented as a function with one weight vector with same "decisions" and "f value". In that case, I'm not sure how the norms of w1 w2 can be merge to one norm without any assumption on the dot product <w1,w2>

Thanx!