Geometry of the Gass-Saaty parametric cost LP algorithm
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In previous discussions of the Gass-Saaty algorithm, the possibility of cycling is avoided by making strong nondegeneracy assumptions or by incorporating a lexicographic decision rule. By analyzing the geometric ideas on which the algorithm is based, it is shown here that even without any “lexicography,” cycling is impossible unless the two objective functions are related in a very special way to each other or to the constraints defining the feasible regionP. In particular, the avoidance of cycling does not require any restriction on the facial structure ofP or on the algebraic relationships among the linear equalities and inequalities by means of whichP is defined.
KeywordsFeasible Region Discrete Comput Geom Linear Functional Simplex Algorithm Polyhedral Cone
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