In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency were generalized to variable ordering structu...

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

We apply a recent characterization of optimality for the abstract convex program with a cone constraint to three matrix theory problems: (1) a generalization of Farkas’s lemma; (2) paired duality in linear programming over cones; (3) a constrained matrix best approximation problem. In particular, these results are not restricted to polyhedral or closed cones.

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

In this paper, we investigate the structure of several convex cones that arise in the study of Lyapunov functions. In particular, we consider cones associated with quadratic Lyapunov functions for both linear and non-linear systems, as well as cones that arise in connection with diagonal and linear copositive Lyapunov functions for positive linear systems. In each of these cases, we present som...

In this paper, the structure of several convex cones that arise in the study of Lyapunov functions is investigated. In particular, the cones associated with quadratic Lyapunov functions for both linear and non-linear systems are considered, as well as cones that arise in connection with diagonal and linear copositive Lyapunov functions for positive linear systems. In each of these cases, some t...

We consider a compound testing problem within the Gaussian sequence model in which the null and alternative are specified by a pair of closed, convex cones. Such cone testing problem arise in various applications, including detection of treatment effects, trend detection in econometrics, signal detection in radar processing, and shape-constrained inference in non-parametric statistics. We provi...

Yan-Bin Jia Michael Erdmann The Robotics Institute School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213-3891 Abstract Industrial assembly involves sensing the pose (orientation and position) of a part. E cient and reliable sensing strategies can be developed for an assembly task if the shape of the part is known in advance. In this paper we investigate the problem of deter...

We show how a recent result of Hrushovsky [6] implies that if an asymptotic cone of a finitely generated group is locally compact, then the group is virtually nilpotent. Let G be a group generated by a finite set X. Then G can be considered as a metric space where dist(g, h) is the length of a shortest word on X ∪X−1 representing g−1h. Let ω be a non-principal ultrafilter on N, i.e. a function ...

This paper gives a survey of embedding theorems for cones and their application to classes of convex sets occurring in interval