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Pivot Rule

In: Linear Programming Computation

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  • Ping-Qi PAN

    (Southeast University, Department of Mathematics)

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.

Suggested Citation

  • Ping-Qi PAN, 2014. "Pivot Rule," Springer Books, in: Linear Programming Computation, edition 127, chapter 0, pages 297-309, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-40754-3_11
    DOI: 10.1007/978-3-642-40754-3_11
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