text: import torch
  from torch.optim.optimizer import Optimizer, required
  
  class SGD(Optimizer):
      """Implements stochastic gradient descent (optionally with momentum).
      Args:
          params (iterable): iterable of parameters to optimize or dicts defining
              parameter groups
          lr (float): learning rate
          momentum (float, optional): momentum factor (default: 0)
          weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
          dampening (float, optional): dampening for momentum (default: 0)
          nesterov (bool, optional): enables Nesterov momentum (default: False)
      """
  
      def __init__(self, params, lr=required, momentum=0, dampening=0,
                   weight_decay=0, nesterov=False):
          if lr is not required and lr < 0.0:
              raise ValueError("Invalid learning rate: {}".format(lr))
          if momentum < 0.0:
              raise ValueError("Invalid momentum value: {}".format(momentum))
          if weight_decay < 0.0:
              raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
  
          defaults = dict(lr=lr, momentum=momentum, dampening=dampening,
                          weight_decay=weight_decay, nesterov=nesterov)
          if nesterov and (momentum <= 0 or dampening != 0):
              raise ValueError("Nesterov momentum requires a momentum and zero dampening")
          super(SGD, self).__init__(params, defaults)
  
      def __setstate__(self, state):
          super(SGD, self).__setstate__(state)
          for group in self.param_groups:
              group.setdefault('nesterov', False)
  
      @torch.no_grad()
      def step(self):
          """Performs a single optimization step.
          """
          loss = None
          for group in self.param_groups:
              weight_decay = group['weight_decay']
              momentum = group['momentum']
              dampening = group['dampening']
              nesterov = group['nesterov']
  
              for p in group['params']:
                  if p.grad is None:
                      continue
                  d_p = p.grad
                  if weight_decay != 0 and p.dim() > 1:
                      d_p = d_p.add(p, alpha=weight_decay)
                  if momentum != 0:
                      param_state = self.state[p]
                      if 'momentum_buffer' not in param_state:
                          buf = param_state['momentum_buffer'] = torch.clone(d_p).detach()
                      else:
                          buf = param_state['momentum_buffer']
                          buf.mul_(momentum).add_(d_p, alpha=1 - dampening)
                      if nesterov:
                          d_p = d_p.add(buf, alpha=momentum)
                      else:
                          d_p = buf
  
                  p.add_(d_p, alpha=-group['lr'])
  
          return loss
  
  