In this paper we introduce the concept of s-monotone index selection rule for linear programming problems. We show that several known anti-cycling pivot rules like the minimal index, Last-In-First-Out and the most-oft...
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In this paper we introduce the concept of s-monotone index selection rule for linear programming problems. We show that several known anti-cycling pivot rules like the minimal index, Last-In-First-Out and the most-often-selected-variable pivot rules are s-monotone index selection rules. Furthermore, we show a possible way to define new s-monotone pivot rules. We prove that several known algorithms like the primal (dual) simplex, MBU-simplex algorithms and criss-cross algorithm with s-monotone pivot rules are finite methods. We implemented primal simplex and primal MBU-simplex algorithms, in MATLAB, using three s-monotone index selection rules, the minimal-index, the Last-In-First-Out (LIFO) and the Most-Often-Selected-Variable (MOSV) index selection rule. Numerical results demonstrate the viability of the above listed s-monotone index selection rules in the framework of pivot algorithms (c) 2012 Elsevier B.V. All rights reserved.
This short discussion paper comments on Francisco Santos' excellent review paper Recent Progress on the Combinatorial Diameter of Polytopes and Simplicial Complexes. We provide some notes on a few closely related ...
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This short discussion paper comments on Francisco Santos' excellent review paper Recent Progress on the Combinatorial Diameter of Polytopes and Simplicial Complexes. We provide some notes on a few closely related topics that were not covered in the survey paper, such as: some relaxed version of the Hirsch conjecture;computability depending on problem data;and continuous versions of the Hirsch conjecture.
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