Extragradient Method for Correction of Inconsistent Linear Programming Problems

Resumo

For a pair of dual inconsistent linear programming problems, the existence and uniqueness of a correction vector that is optimal in the norm is proved. It is shown that the correction problem is reduced to the problem of finding a saddle point of a regularized Lagrange function. A modified extragradient method is proposed for solving the latter problem, and its convergence is proved.