The optimization problem has a fractional of polynomials as the objective function, with linear constraint. For example,
$\min\limits_{x,y}\quad f(x,y)=\sum_{i=1}^N\gamma_i\frac{a_ix^2y+b_ix^2+c_ixy^2+d_iy^2+e_ixy+f_ix+g_iy}{A_ix^3y^2+B_ix^3y+C_ix^2y^2+D_ix^3+E_ix^2y+F_ixy^2+G_ix^2+H_iy^2+I_ixy+J_ix+K_iy}\\ s.t.\quad ax+by\le c,\\ \quad \quad \quad x>0,y>0.$
I am wondering whether this belongs to a certain type of nonlinear optimization problem, and if there is any way to solve this efficiently? Thanks.