The central path visits all the vertices of the Klee-Minty cube
نویسندگان
چکیده
Optimization Methods and Software Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713645924 The central path visits all the vertices of the Klee-Minty cube Antoine Deza a; Eissa Nematollahi a; Reza Peyghami a; Tamás Terlaky a a Advanced Optimization Laboratory, Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada
منابع مشابه
How good are interior point methods? Klee-Minty cubes tighten iteration-complexity bounds
By refining a variant of the Klee–Minty example that forces the central path to visit all the vertices of the Klee–Minty n-cube, we exhibit a nearly worst-case example for path-following interior point methods. Namely, while the theoretical iteration-complexity upper bound is O(2nn 5 2 ), we prove that solving this n-dimensional linear optimization problem requires at least 2n − 1 iterations.
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By introducing some redundant Klee-Minty constructions, we have previously shown that the central path may visit every vertex of the Klee-Minty cube having 2 − 2 “sharp” turns in dimension n. In all of the previous constructions, the maximum of the distances of the redundant constraints to the corresponding facets is an exponential number of the dimension n, and those distances are decaying geo...
متن کاملAdvanced Optimization Laboratory Title: A Redundant Klee-Minty Construction with All the Redundant Constraints Touching the Feasible Region
By introducing some redundant Klee-Minty constructions, we have previously shown that the central path may visit every vertex of the Klee-Minty cube having 2 − 2 “sharp” turns in dimension n. In all of the previous constructions, the maximum of the distances of the redundant constraints to the corresponding facets is an exponential number of the dimension n, and those distances are decaying geo...
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By introducing redundant Klee-Minty examples, we have previously shown that the central path can be bent along the simplex path. In this paper, we seek for an analogous result for the volumetric path defined by the volumetric barrier function. Although we only have a complete proof in 2D, the evidence provided by some illustrations anticipates that a KleeMinty construction exists for the volume...
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ورودعنوان ژورنال:
- Optimization Methods and Software
دوره 21 شماره
صفحات -
تاریخ انتشار 2006