The normalized method of finite penalties in nonlinear programming problems

In the solution of complex problems of conditional optimization a significant role is played by sequential quadratic programming (QP) and linear programming (LP) methods, for which the properties inherent in first-order unconditional optimization methods (nonlocal convergence, estimates of rate of convergence, solvability of auxiliary problems, and so on) have not yet been rigorously established. This question was investigated for methods with an auxiliary QP-problem. However, the known LP-algorithms having such properties either use two auxiliary LP-problems in each iteration, or depend strongly on the choice of the parameters in the ‘•-descent’’ strategy, and this reduces their effectiveness. This note proposes a method, with normalization in each iteration of a certain auxiliary LP-problem, that completely solves the original problem.