Methods of search for stable solutions of some optimization problems in the theory of recognition by precedents

In constructing some models of recognition algorithms, there arise a number of optimization problems. The search for the optimal consistent subsystem of a given system of linear inequalities plays an important role in the process of data analysis in the theory of recognition by precedent. The optimality of a required subsystem is defined by a number of the conditions imposed on it. Earlier the author developed several algorithms for solving the problems of this type. These algorithms are based on exhaustive search for nodal subsystems of a given system of linear inequalities. In the search for optimal consistent subsystem, these algorithms find boundary decisions. However, in practical application often it is necessary to find a stable solution. So, when looking for logical regularities of a special type, it is required to find a set of non-degenerate polyhedra describing a certain class of objects in a space of features. Therefore, linear inequalities systems corresponding to these polyhedra must be stable. In this paper, we propose a method for modifying the previously developed algorithms to select the stable consistent subsystem of highest possible power and find its stable solution.