  We introduce and study exterior distance function (EDF) and correspondent
exterior point method (EPM) for convex optimization.
  The EDF is a classical Lagrangian for an equivalent problem obtained from the
initial one by monotone transformation of both the objective function and the
constraints.
  The constraints transformation is scaled by a positive scaling parameter.
Thus, the EDF is a particular realization of the Nonlinear Rescaling (NR)
principle.
  Along with the "center", the EDF has two extra tools: the barrier (scaling)
parameter and the vector of Lagrange multipliers.
  We show that EPM generates primal - dual sequence, which converges to the
primal - dual solution in value under minimum assumption on the input data.
Moreover, the convergence is taking place under any fixed interior point as a
"center" and any fixed positive scaling parameter, just due to the Lagrange
multipliers update.
  If the second order sufficient optimality condition is satisfied, then the
EPM converges with Q-linear rate under any fixed interior point as a "center"
and any fixed, but large enough positive scaling parameter.
