A modified limited memory Nesterov's accelerated quasi-Newton

The Nesterov's accelerated quasi-Newton (L)NAQ method has shown to accelerate the conventional (L)BFGS quasi-Newton method using the Nesterov's accelerated gradient in several neural network (NN) applications. However, the calculation of two gradients per iteration increases the computational cost. The Momentum accelerated Quasi-Newton (MoQ) method showed that the Nesterov's accelerated gradient can be approximated as a linear combination of past gradients. This abstract extends the MoQ approximation to limited memory NAQ and evaluates the performance on a function approximation problem.