Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...

Let P be a polyhedron in H$ of finite volume such that the group Γ(P) generated by reflections in the faces of P is a discrete subgroup of IsomH$. Let Γ+(P) denote the subgroup of index 2 consisting entirely of orientation-preserving isometries so that Γ+(P) is a Kleinian group of finite covolume. Γ+(P) is called a polyhedral group. As discussed in [12] and [13] for example (see §2 below), asso...

I’m trying to understand which Riemannian manifolds can be Lipschitz approximated by polyhedral spaces of the same dimension with curvature bounded below. The necessary conditions I found consist of some special inequality for curvature at each point (the geometric curvature bound). This inequality is also sufficient condition for local approximation. I conjecture that it is also a sufficient c...

iii Acknowledgments iv Chapter 1. A Hierarchy of Polyhedral Arrangements 1 1.1. Polyhedral Arrangements 1 1.2. Polyhedral Dissections 1 1.3. Polyhedral Complexes 5 1.4. Polyhedral Triangulations 8 1.5. A Hierarchy of Polyhedral Arrangements 9 Chapter 2. Computation on Polyhedral Arrangements 12 2.1. Bucket Method 12 2.2. Sage Code 13 2.3. Experiments 16 Chapter 3. Regular Triangulations 22 3.1....

...................................................................................................................... xv Résumé .................................................................................................................... xvii 摘 要 ......................................................................................................................xix Introduction ..........