We study subgroups of SL ( 3 , R ) ⋉ $\mathrm{SL}(3,\mathbb {R})\ltimes \mathbb {R}^3$ obtained by adding a translation part to the holonomy finite-volume convex projective surface. Under natural condition on translations added peripheral parabolic elements, we show that affine action group $\mathbb has domains discontinuity which are regular, generalizing result Mess for globally hyperbolic fl...

Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an...

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 begin with a lattice N isomorphic to Z. The dual lattice M of N is given by Hom(N,Z); it is also isomorphic to Z. (The alphabet may appear to be going backwards; but this notation is standard in the literature.) We write the pairing of v ∈ N and w ∈M as 〈v, w〉. A cone in N is a subset of the real vector space NR = N ⊗R generated by nonnegative R-linear combinations of a set of vectors {v1, ....

This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone K, a logarithmically homogeneous self-concordant barrier for K and any positive real number r ≤ 1, we associate, with each direction x ∈ K, a second-order cone K̂r(x) containing K. We show that K is the intersection of the second-order cones K̂r(x), as x ranges through ...

The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard constraint qualificatio...

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.

Abstract Amenability is a notion of facial exposedness for convex cones that stronger than being facially dual complete (or ‘nice’) which is, in turn, merely exposed. Hyperbolicity are family algebraically structured closed contain all spectrahedral (linear sections positive semidefinite cones) as special cases. It known amenable. We establish hyperbolicity As part the argument, we show any fac...