THEOREMS OF ALTERNATIVE AND FEASIBILITY/INFEASIBILITY IN MATHEMATICAL PROGRAMMING
EVALD UBI *
Tallinn University of Technology, Estonia.
JAAN UBI *
The University of Tartu, Estonia.
*Author to whom correspondence should be addressed.
In this review paper we consider the conditions of solvability of extremal problems with linear constraints. These are derived from the classical theorems of the alternative. In addition we look at nding the initial solution of a linear programming problem and a new version of the artificial basis method, as well as solving least-squares problems and quadratic programming problems. The main ideas are explained by simple examples.
Keywords: Theorem of alternative, system of linear inequalities, nonnegative solution to the system of linear equations, artificial basis method, method of least squares