code: def _optimize_simplex(gamma, v, lambda_v, opt_x, s=1):
      opt_x_old = np.copy(opt_x)
      f_old = _f_simplex(gamma, v, lambda_v, opt_x)
      df = _df_simplex(gamma, v, lambda_v, opt_x)
      ab_sum = np.sum(np.absolute(df))
      if ab_sum > 1.0:
          df /= ab_sum
      opt_x -= df
      x_bar = _simplex_project(opt_x, s=s)
      x_bar -= opt_x_old
      r = 0.5 * np.dot(df, x_bar)
      beta = 0.5
      t = beta
  
      for iter in range(100):
          opt_x = np.copy(opt_x_old)
          opt_x += t * x_bar
          f_new = _f_simplex(gamma, v, lambda_v, opt_x)
          if f_new > f_old + r * t:
              t *= beta
          else:
              break
  
      if not _is_on_simplex(opt_x, s):
          print("Invalid values, outside simplex")
  
      return opt_x, f_new
  
file_path: cornac/cornac/models/ctr/ctr.py
imports: import numpy
  from ...utils import get_rng
label_desc: Use image node_id 5 for calling a global function with example usage: _optimize_simplex(gamma, v, lambda_v, opt_x, s) and returns: opt_x,  f_new