Discriminant analysis and randomization in linear optimization problems with unformalized constraints

Abstract

A linear optimization problem with an unformalized constraint (LOPUC) is considered. An iterative approach is proposed in which an approximate solution to a LOPUC is obtained by a successive discriminant analysis of the available set of precedents and by examination of newly obtained samples. An algorithm is described for the generation of samples by solving an approximation linear programming problem (ALPP) that is obtained by adding an inequality defined by a discriminant function to the formalized part of the LOPUC. For the algorithm proposed, the convergence of the sequence of approximate solutions to the exact solution of the LOPUC is proved.