Relevant and irrelevant documents share some terms (at least the terms of the query which selected these documents). The majority of relevance feedback methods try to optimally separate relevant and irrelevant documents; indeed, these methods build a new set of indexing terms (vector space basis) which separate these documents. But there is no satisfactory answer to this problem. In this paper, we propose to separate relevant and irrelevant documents using Lagrange multipliers. This new approach is evaluated experimentally on two TREC collections (TREC-7 ad hoc and TREC-8 ad hoc). The experiments show that this method improves previous works.