NP-hardness of a bilinear program?
Your objective is to minimize the convex function $-\sum_{i=1}^n(x_i−a_i)y_i$ subject to a system of linear constraints on the continuous variables $x_i$ and $y_i$.

Such convex minimization problems are polynomially solvable by so-called interior point methods; see for instance the book by Stephen Boyd and Lieven Vandenberghe: "Convex Optimization"; free pdf copy at: http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf