The method of conditional minimization based on the selection of the optimal value of the objective function

Abstract

© Published under licence by IOP Publishing Ltd. One of the convex programming methods that allows to reduce the solution of the original problem to the successive minimization of auxiliary functions on the whole space or on simple sets is the method of parametrization of the objective function. A method close to the one mentioned above is proposed in this paper. As in the known method, in order to find an iterative point, we solve the minimization problem of some auxiliary function constructed with cuts of the parametrized objective function and the constraint functions. The proposed method has some advantages over the parametrization method of the objective function due to a different principle of setting parameter values. The method convergence is substantiated. The properties associated with its implementation are discussed.