text: abstract. the big data phenomenon has spawned large-scale linear
  programming problems. in many cases, these problems are non-stationary. in this paper, we describe a new scalable algorithm called nslp
  for solving high-dimensional, non-stationary linear programming problems on modern cluster computing systems. the algorithm consists of
  two phases: quest and targeting. the quest phase calculates a solution
  of the system of inequalities defining the constraint system of the linear programming problem under the condition of dynamic changes in
  input data. to this end, the apparatus of fejer mappings is used. the
  targeting phase forms a special system of points having the shape of an
  n-dimensional axisymmetric cross. the cross moves in the n-dimensional
  space in such a way that the solution of the linear programming problem
  is located all the time in an ε-vicinity of the central point of the cross.
  keywords: nslp algorithm · non-stationary linear programming problem · large-scale linear programming · fejer mapping.