In 1960, Klee showed that a subset of a Euclidean space must be a singleton provided that each point in the space has a unique farthest point in the set. This classical result has received much attention; in fact, the Hilbert space version is a famous open problem. In this paper, we consider Klee sets from a new perspective. Rather than measuring distance induced by a norm, we focus on the case...

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 Un...

Devising a reproducible approach for species delimitation of hyperdiverse groups is an ongoing challenge in evolutionary biology. Speciation processes combine modes of passive and adaptive trait divergence requiring an integrative taxonomy approach to accurately generate robust species hypotheses. However, in light of the rapid decline of diversity on Earth, complete integrative approaches may ...

We analyse the security of code by extending the KLEE symbolic execution engine with a tainting mechanism that tracks information flows of data. We consider both simple flows from direct assignment operations, and (more subtle) indirect flows inferred from the control flow. Our mechanism prevents overtainting by using a region-based static analysis provided by LLVM, the compiler infrastructure ...

We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the Klee-Minty cubes 16] and similar linear programs with exponential decreasing paths. The analysis of two randomized pivot rules on the Klee-Minty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus ...

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...

A Banach space has the weak fixed point property if its dual space has a weak∗ sequentially compact unit ball and the dual space satisfies the weak∗ uniform Kadec-Klee property; and it has the fixed point property if there exists ε > 0 such that, for every infinite subset A of the unit sphere of the dual space, A ∪ (−A) fails to be (2 − ε)-separated. In particular, E-convex Banach spaces, a cla...

Let K be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1, T2, . . . , TN : K −→ E be N asymptotically nonexpansive nonself mappings with sequences {r n} such that ∑∞ n=1 r n < ∞, for all 1 ≤ i ≤ N and F = ∩i=1F (Ti) 6= φ. Let {α n}, {β n} and {γ n} are sequences in [0, 1] with α n + β i n + γ i n = 1 for all i =...

A fixed-point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subset of a t.v.s. is applied to obtain a cyclic coincidence theorem for acyclic maps, generalized “onNeumann type intersection theorems, the Nash type equilibrium theorems, and the “onNeumann minimax theorem. Our new results generalize earlier works of Lassonde [l], Simons [2], and Park [3...