Analysis of Interior-Point Methods for Linear Programming Problems with Variable Upper Bounds

We describe path-following and potential-reduction algorithms for linear programming problems with variable upper bounds. Both methods depend on a barrier function for the cone of solutions to the variable upper bounds, and we establish the key properties of this barrier that allow the complexity of the algorithms to be analyzed. These properties mostly follow from the self-concordance of the function, a notion introduced by Nesterov and Nemirovsky. Our analysis follows that of Freund and Todd for problems with (possibly two-sided) simple bounds.

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