Two modifications of the linearization method in nonlinear programming

In Pshenichnii's linearization method for solving the general problem of non-linear programing, an auxiliary quadratic programming problem is solved at each step. In the two modifications of the linearization method described below, auxiliary problems of linear programming are solved. The properties of these auxiliary problems are studied, the convergence of the methods to the solution of the non-linear programming problem is proved, and features of their numerical realization are discussed.