Adduced direction method based on modified Lagrange function for problem of nonlinear programming (Q1380194)

We suggest a further development of a unified approach to the construction of methods for solving nonlinear programming problems on the basis of the notion of adduced direction. Together with the penalty functions technique, that of possible directions, and methods of differentiable penalty functions, in a unified scheme of methods of adduced directions both the new method as well as known methods of modified Lagrange functions are suggested on the basis of payoff functions. The suggested new method of modified Lagrange functions is based on a specific way to construct an index set of ``active'' constraints and on the procedure of estimation of Lagrange multipliers at iteration points. In contrast to the known methods of modified Lagrange functions we do not use here the auxiliary procedure of the unconditional minimization of the payoff function. It is shown that, under a certain choice of parameters, in frames of unified scheme the method of recursive quadratic programming can be realized on the basis of the payoff function, which is used in solving degenerated problems. The exposed methods were realized as a software and are included into the optimization dialogue software system ODiS as well as into a methodical software complex for studying optimization methods.