Abstract
A barrier formulation of interior point methods for the linear programming problem is considered. It is shown that a dual feasible vector can be constructed provided the Newton iterates satisfies a slightly stronger condition than feasibility. The duality gap computed using this data is strictly smaller than that obtained by running the Newton iteration to convergence. Thus this condition provides a new stopping criterion for the barrier function based interior point methods for linear programming. An O(nL) estimate for the number of steps to termination is derived. Numerical experience is reported for a method in which the barrier parameter is modified adaptively in an attempt to keep the number of Newton iterations per step fixed.Key wordsbarrier functioninterior point methodNewton’s methodstopping criterionreduced duality gappolynomial complexity
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