Interior penalty functions and duality in linear programming

Abstract

Logarithmic additive terms of barrier type with a penalty parameter are included in the Lagrange function of a linear programming problem. As a result, the problem of searching for saddle points of the modified Lagrangian becomes unconstrained (the saddle point is sought with respect to the whole space of primal and dual variables). Theorems on the asymptotic convergence to the desired solution and analogs of the duality theorems for the arising optimization minimax and maximin problems are formulated. © 2013 Pleiades Publishing, Ltd.