Pivot Rule

Ping-Qi Pan
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Ping-Qi Pan: Southeast University, Department of Mathematics

Chapter Chapter 11 in Linear Programming Computation, 2014, pp 297-309 from Springer

Abstract: Abstract A pivot rule plays a crucial role in the simplex method for solving the standard LP problem. Starting from a vertex of the feasible region, geometrically the method moves from a vertex to adjacent vertex until reaching an optimal vertex. The related “path” consists of a series of edges (which could vanish in the presence of degeneracy), joining or be joined end to end. The number of edges, termed the “length” of the path, is equal to the number of iterations taken by the simplex method. It is the pivot rule that specifies a edge to move along in each iteration, and hence determines the number of required iterations, theoretically. Indeed, the pivot rule is the characteristic or spirit of the simplex method.

Keywords: Price Option; Simplex Method; Time Ratio; Column Index; Reference Framework (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-642-40754-3_11

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