Nocuous ambiguity occurs when a linguistic expression is interpreted differently by different readers in a given context. We present an approach to automatically identify nocuous ambiguity that is likely to lead to misunderstandings among readers. Our model is built on a machine learning architecture. It learns from a set of heuristics each of which predicts a factor that may lead a reader to f...

We propose a Bayesian framework for assessing the relative strengths of data-driven ambiguity sets in distributionally robust optimization (DRO) when the underlying distribution is defined by a finite-dimensional parameter. The key idea is to measure the relative size between a candidate ambiguity set and a specific, asymptotically optimal set. This asymptotically optimal set is provably the sm...

Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. The approach exploits a recently developed DC (Difference of Convex functions) programming technique developed by the authors to construct a polyhedral set in between two convex sets. Here, the inner convex set is any given level set V (x...

We study rigidity of polyhedral surfaces and the moduli space of polyhedral surfaces using variational principles. Curvature like quantities for polyhedral surfaces are introduced. Many of them are shown to determine the polyhedral metric up to isometry. The action functionals in the variational approaches are derived from the cosine law and the Lengendre transformation of them. These include e...

Introduction Propose and provide foundations for a preference model set in an explicitly dynamic framework with uncertainty where: DM is sensitive to ambiguity ambiguity attitude is separated from ambiguity ‡exibility in ambiguity attitude and in scope of ambiguity preferences are dynamically consistent discounted expected utility is a special case beliefs are updated over time

This article studies the polyhedral structure of the 4-node network design problem (NDP). Using a theorem from the previous work of this author, the facets of the 4-node NDP can be translated into facets of larger size problems. The knowledge of complete polyhedral description of the 4-node NDP is important because it implies complete knowledge of 4-partition-based facets of larger NDPs. After ...

This report introduces a new approach to discrete optimization, based on the insights of polyhedral combinatorics, and compares it to approaches used in mathematical programming, computational geometry and database systems. It presents an algorithm based on the polyhedral approach solving the following linear discrete optimization problem: preprocess a set of points in three dimensions in a way...

We consider optimization problems with some binary variables, where the objective function is linear in these variables. The stability region of a given solution is the polyhedral set of objective coefficients for which the solution is optimal. Knowledge of this set provides valuable information for sensitivity analysis and re-optimization. An exact description of the stability region may requi...

Loss Set A Set A Set A Set A Investment Set B Set B Set B Set B Insurance Set B Set B Set B Set B Furthermore, the subjects face four different types of information in both decision frames and treatments. The ‘precise’ information frame has exact probabilities and exact payments stated. In the ‘ambiguity in probability’ frames, the probability is stated as a range and the payment is fixed. Conv...

The Sparse Polyhedral Framework (SPF) extends the Polyhedral Model by using the uninterpreted function call abstraction for the compile-time specification of run-time reordering transformations such as loop and data reordering and sparse tiling approaches that schedule irregular sets of iteration across loops. The Polyhedral Model represents sets of iteration points in imperfectly nested loops ...