On the structure of the conditional εà-subgradient method for simultaneous solution of the direct and dual convex programming problems

The investigation of the sensitivity of a solution obtained for the convex programming problem to various kinds of computational errors presumes that a Kuhn-Tucker vector has been found (a solution of the dual problem). Moreover, the necessity of computing this vector can be stipulated by the very nature of the problem, for example, when in the framework of the corresponding economic model the components of the Kuhn-Tucker vector are interpreted as ‘equilibrium prices’ of the available resources or producible goods. The computation of estimates of a Kuhn-Tucker vector is specified or can be carried out in a large group of mathematical programming methods. The paper considers a convex programming problem such that to find a solution of it with the simultaneous computation of estimates of a Kuhn-Tucker vector the traditional approaches can turn out to be inefficient or even unsuitable. Basically, this has to do with the absence of assumptions about the differentiability of the functions making up the problem and about the existence of some structure for it. Moreover, the function to be minimized in the case under consideration can fail to be defined outside the admissible set of the problem.