Matrix Correction of a Dual Pair of Improper LinearProgramming Problems with a Block Structure

摘要

Modifying improper linear programs (LPs) with a block structure is a fairly important task. For instance,it may arise in modeling certain economic systems consisting of loosely connected smaller subsystems withtheir own resource sets and their own output. If the block systems of constraints are inconsistent, the corre-sponding LPs become improper. For such LPs, the problem of matrix correction has the characteristic fea-ture that corrections must also be block matrices; moreover, if a block in the original coefficient matrix iszero, then the corresponding block in the correction matrix must also be zero.