Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson’s outer approximation algorithm, and the second one is a dual variant of it. Both algorithms provide an inner as well as an outer approximation of the (upper and lower) image...

We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P ∈ R by its dual Lp-centroid bodies is independent of the geometry of P . In particular we show that if P has volume 1, lim p→∞ p log p „ |Z◦ p (P )| |P ◦| − 1 « = n. We provide an application to the approximation of polytopes by uniformly convex sets.

We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P ∈ R by its dual Lp-centroid bodies is independent of the geometry of P . In particular we show that if P has volume 1, lim p→∞ p log p „ |Z◦ p (P )| |P ◦| − 1 « = n. We provide an application to the approximation of polytopes by uniformly convex sets.

A common fixed-point generalization of the results of Dotson, Tarafdar, and Taylor is obtained which in turn extends a recent theorem by Jungck and Seasa to locally convex spaces. As applications of our work, we improve and unify well-known results on fixed points and common fixed points of beat approximation. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords--common fixed point, Best ...

Let U ⊆ R be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function f : U → R can be approximated by real analytic convex functions, uniformly on all of U . We also show that C-fine approximation of convex functions by smooth (or real analytic) convex functions on R is possible in general if and only if d = 1. Nevertheless, for d ≥ 2 we give a characterizat...

The paper is an updated survey of our work on the approximation of univariate setvalued functions by samples-based linear approximation operators, beyond the results reported in our previous overview. Our approach is to adapt operators for real-valued functions to set-valued functions, by replacing operations between numbers by operations between sets. For set-valued functions with compact conv...

It is known that the bandwidth problem is NP-complete for chordal bipartite graphs, while the problem can be solved in polynomial time for bipartite permutation graphs, which is a subclass of chordal bipartite graphs. This paper shows that the problem is NP-complete even for convex bipartite graphs, a subclass of chordal bipartite graphs and a superclass of bipartite permutation graphs. We prov...

The strong convergence of a broad class of outer approximation methods for minimizing a convex function over the intersection of an arbitrary number of convex sets in a reflexive Banach space is studied in a unified framework. The generic outer approximation algorithm under investigation proceeds by successive minimizations over the intersection of convex supersets of the feasibility set determ...