Problems with Nonnegativity Constraints

Abstract

Now we deal with linear programming problems of the type

$$ _{\begin{subarray}{l} subject\;to\quad a_1^T \leqslant 1, \ldots, a_m^Tx \leqslant 1,x \geqslant 0 \\ where\;\quad \quad x,{a_{{1,}}} \ldots, {a_m},v \in {\mathbb{R}^n} \end{subarray} }^{{Maximize\quad {v^T}x}} $$

. Here the feasibility region will be denoted by X^. The origin is — in any case — a vertex of X^ and can be used as an initial vertex. Hence Phase I is superfluous.