Extensions of Antipodal-Type Theorems

Autor: Viacheslav Kalashnikov, Lilia Alanis-Lopez, A.J.J. Talman, Nataliya I. Kalashnykova

Publikováno v: 2018 International Conference on Unconventional Modelling, Simulation and Optimization - Soft Computing and Meta Heuristics - UMSO.

The paper develops the extensions of both the antipodal (Borsuk–Ulam) theorem and Browder theorem to the cases embracing star-shaped domains of the studied mappings and a multi-valued nature of the latter.To be more specific, by making use of the t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d4c439e94c0b8ea9d994a3ed7450b599
https://doi.org/10.1109/umso.2018.8637224

Combinatorial integer labeling theorems on finite sets with applications

Autor: A.J.J. Talman, Zaifu Yang, G. van der Laan

Publikováno v: Journal of Optimization Theory and Applications, 144, 391-407. Springer New York
Journal of Optimization Theory and Applications, 144, 391-407. SPRINGER/PLENUM PUBLISHERS
van der Laan, G, Talman, A J J & Yang, Z 2010, ' Combinatorial integer labeling theorems on finite sets with applications ', Journal of Optimization Theory and Applications, vol. 144, pp. 391-407 . https://doi.org/10.1007/s10957-009-9603-7

Tucker's well-known combinatorial lemma states that, for any given sym- metric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1, ±2 ,..., ±n} with t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9a9ea7ee917d5f74c6cf8b60113e9537
https://doi.org/10.1007/s10957-009-9603-7

A constructive proof of Ky Fan’s coincidence theorem

Autor: Zaifu Yang, A.J.J. Talman

Publikováno v: Mathematical Programming. 118:317-325

We present a constructive proof for the well-known Ky Fan’s coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c4f5ee8297150464c2e428283c754f3a
https://doi.org/10.1007/s10107-007-0194-5

Continuum of Zero Points of a Mapping on a Compact, Convex Set

Autor: Yoshitsugu Yamamoto, A.J.J. Talman

Publikováno v: SIAM Journal on Optimization. 14:1128-1139

Let X be a nonempty, compact and convex set in Rn and $\phi$ be an outer semicontinuous mapping from X to the collection of nonempty, compact convex subsets of Rn. We show that for any nonzero vector c in Rn there exists a set of stationary points of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::85081b0e82801e816eae391a8ed20a3f
https://doi.org/10.1137/s1052623402415469

Intersection Theorems with a Continuum of Intersection Points

Autor: P.J.J. Herings, A.J.J. Talman

Publikováno v: Journal of Optimization Theory and Applications, 96(2), 311-335. SPRINGER/PLENUM PUBLISHERS

In all existing intersection theorems, conditions are given under which a certain subset of a collection of sets has a nonempty intersection. In this paper, conditions are formulated under which the intersection is a continuum of points satisfying so

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a3e6cbc5fee736edc70aa4ba76bce992
https://doi.org/10.1023/a:1022618130893