作者：Scholtes, S
摘要：This article is mainly concerned with the homeomorphism problem for piecewise affine mappings (PA-maps), i.e., mappings which coincide with an affine mapping on each polyhedron of some finite polyhedral subdivision of R(n). In the first part, we prove that a PA-map can be defined without referring to a subdivision of R(n) as a continuous mapping which coincides at every point x is an element of R(n) with al least one function from a finite collection of affine functions. The second part studie...
作者：Guler, O
摘要：We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides a simple method for calculating the universal barrier for homogeneous cones. We identify some known barriers as the universal barrier scaled by an appropriate constant. We also calculate some new u...
作者：Flesch, J; Thuijsman, F; Vrieze, OJ
摘要：We show the existence of stationary limiting average epsilon-equilibria (epsilon > 0) for two-person recursive repeated games with absorbing states. These are stochastic games where all states but one are absorbing, and in the nonabsorbing state ail payoffs are equal to zero. A state is called absorbing if the probability of a transition to any other state is zero for all available pairs of actions. For the purpose of our proof, we introduce properness for stationary strategy pairs. Our result...
