New algorithms for linear programming (Q1207191)

The linear programming problem of the form \(\min c^ T x\), subject to \(Ax=b\), \(0\leq x\leq d\), is converted into a nonlinear unconstrained maximization problem with a concave objective function. Two algorithms are proposed for solving this unconstrained maximization problem. The first one uses the gradient method, the second one the variable metric method. Both algorithms terminate in a finite number of steps for any given accuracy.