  Multinomial logistic regression, also known by other names such as multiclass
logistic regression and softmax regression, is a fundamental classification
method that generalizes binary logistic regression to multiclass problems. A
recently work proposed a faster gradient called $\texttt{quadratic gradient}$
that can accelerate the binary logistic regression training, and presented an
enhanced Nesterov's accelerated gradient (NAG) method for binary logistic
regression.
  In this paper, we extend this work to multiclass logistic regression and
propose an enhanced Adaptive Gradient Algorithm (Adagrad) that can accelerate
the original Adagrad method. We test the enhanced NAG method and the enhanced
Adagrad method on some multiclass-problem datasets. Experimental results show
that both enhanced methods converge faster than their original ones
respectively.
