Quadratic programming and combinatorial minimum weight product problems

We present a fully polynomial time approximation scheme (FPTAS) for minimizing an objective (aT x + ¿)(bTx + d) under linear constraints Ax = d. Examples of such problems are combinatorial minimum weight product problems such as, e.g., the following: Given a graph G = (V,E) and two edge weights a, b : E ¿ R+ find an s-t path P that minimizes a(P)b(P), the product of its edge weights relative to a and b