3. The Double Description Method

@inproceedings{Motzkin19533TD,
  title={3. The Double Description Method},
  author={Theodore S. Motzkin and Howard Raiffa and Gerald L. Thompson and Robert M. Thrall},
  year={1953}
}
Static Analysis
TLDR
Interpretation of Stateful Networks: Towards an Efficient Abstract Domain for Not Necessarily Closed Polyhedra.
New modification of the double description method for constructing the skeleton of a polyhedral cone
A new modification of the double description method is proposed for constructing the skeleton of a polyhedral cone. Theoretical results and a numerical experiment show that the modification is
Average-Case Analysis of the Double Description Method and the Beneath-Beyond Algorithm
TLDR
The average-case analysis is done with respect to the Rotation-Symmetry Model, which is well known from the corresponding analysis of the Simplex Method for linear programming.
Static Analysis: 26th International Symposium, SAS 2019, Porto, Portugal, October 8–11, 2019, Proceedings
TLDR
This paper presents a corpus of invited contributions towards Semantic Adversarial Examples that describes the development of semantic adversarial models in the context of knowledge representation.
Algorithms for on-line vertex enumeration problem
  • I. Kaya
  • Mathematics, Computer Science
  • 2017
TLDR
This thesis considers the 'double description method' which is a method to solve an on-line vertex enumeration problem where the starting polyhedron is bounded and generates an iterative algorithm to solve the vertex enumerations problem from the scratch wherepolyhedron P is allowed to be bounded or unbounded.
Beyond Correlation: Measuring Interdependence Through Complementarities
Given two sets of random variables, how can one determine whether the former variables are more interdependent than the latter? This question is of major importance to economists, for example, in
Polyhedral Analysis Using Parametric Objectives
TLDR
An algorithm to calculate variable elimination (projection) based on parametric linear programming, which enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output.
Increasing interdependence of multivariate distributions
PRIMA: general and precise neural network certification via scalable convex hull approximations
TLDR
The results show that PRIMA is significantly more precise than the state-of-the-art, verifying robustness to input perturbations for up to 20%, 30%, and 34% more images than existing work on ReLU-, Sigmoid-, and Tanh-based networks, respectively.
Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors
TLDR
Different methods for obtaining a feasible parameter set are evaluated for the use with Takagi-Sugeno models and case studies with simulated data and with measured data from a manufacturing process are presented.
...
...