Some new results on the algebraic characterizations of an equality constrained optimization problem equivalent to the transportation problem

Abstract

An equality constrained optimization problem equivalent to the transportation problem with m sources and n destinations is described. The optimality condition and some algebraic characterizations of the problem are investigated using its Hessian matrix. In addition, several algebraic characterizations of an equivalent case of the transportation problem are given using the spectral decomposition and generalized inverses of its coefficient matrix. It is shown that the transportation problem and its equivalent case have common algebraic characterizations.

Keywords:

• Linear programming
• Transportation problem
• Equality constrained optimization problem
• Spectral decomposition
• Hessian matrix