Optimization methods for a non-quadratic model

This paper reviews the state of the art and future development on non-quadratic model optimization (NQMO). Optimization methods based on the non-quadratic model are more interesting than ones based on the quadratic model because they have more interpolation information and better approximation effect, especially for ill-conditioned functions or functions with strong non-quadratic behaviour. The main non-quadratic model methods include conic model methods, homogeneous model methods, nonlinear scaling model methods, tensor model methods and trust region model methods. The paper thinks that further study of NQMO is necessary, the area shows great potential and it is interesting.