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Excerpt from Determination of Optimal Vertices From Feasible Solutions in Unimodular Linear Programming <p>In this paper we consider the problem of determining optimal solutions of this linear program from information derived from a given pair of primal and dual near optimum feasible solutions. An example of such a result is the strong duality theorem which asserts that if the objective function value of the given primal solution is equal to the objective function value of the given dual solution, then we can declare the pair to be optimal for the respective problems. Here we investigate the problem -of determining optimal vertices of the two problems given that the difference in the objective function values i.e., the duality gap is greater than zero. For the special case of unimodular systems, under the hypothesis that the duality gap is small not necessarily zero we obtain results that assert the integrality of variables in Optimal solutions. An example of such a result Corollary 3 is that if the duality gap is less than and the Optimum solution of the program is unique, then the optimum vertex can be obtained by a simple rounding routine. <p>About the Publisher <p>Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com <p>This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.