[HTML][HTML] Solving the fixed rank convex quadratic maximization in binary variables by a parallel zonotope construction algorithm
JA Ferrez, K Fukuda, TM Liebling - European Journal of Operational …, 2005 - Elsevier
We address the weighted max-cut problem, or equivalently the problem of maximizing a
quadratic form in n binary variables. If the underlying (symmetric) matrix is positive semidefinite …
quadratic form in n binary variables. If the underlying (symmetric) matrix is positive semidefinite …
Representation of polytopes as polynomial zonotopes
N Kochdumper, M Althoff - arXiv preprint arXiv:1910.07271, 2019 - arxiv.org
… present in this paper is based on polynomial zonotopes, a non-convex set … zonotopes from
[17]. Taylor Models are a type of set representation closely related to polynomial zonotopes […
[17]. Taylor Models are a type of set representation closely related to polynomial zonotopes […
Zonotope dynamics in numerical quality control
W Kühn - Mathematical Visualization, 1998 - Springer
… We present a new method which constructs high order zonotope (special polytopes) … the
order of the zonotopes. The method induces in the space of zonotopes a dynamical system of …
order of the zonotopes. The method induces in the space of zonotopes a dynamical system of …
[HTML][HTML] A comparison of zonotope order reduction techniques
… for enclosing a given zonotope within another of lower … in recursive computations with
zonotopes and are widely used … , and investigate the effects of zonotope dimension, initial order, …
zonotopes and are widely used … , and investigate the effects of zonotope dimension, initial order, …
[HTML][HTML] On the co-NP-completeness of the zonotope containment problem
A Kulmburg, M Althoff - European Journal of Control, 2021 - Elsevier
… non-degenerate zonotopes to solve the … zonotope containment problem exactly in polynomial
time when fixing the dimension or the number of generators of either of the two zonotopes. …
time when fixing the dimension or the number of generators of either of the two zonotopes. …
[PDF][PDF] Cuts, zonotopes and arrangements
JA Ferrez, K Fukuda, TM Liebling - The sharpest Cut. SIAM Series …, 2001 - researchgate.net
… This object is known as a zonotope. … In particular, we propose a more efficient modification
of the reverse search algorithm [2] for generating all extreme points of a given zonotope in Êd, …
of the reverse search algorithm [2] for generating all extreme points of a given zonotope in Êd, …
Identification for passive robust fault detection using zonotope‐based set‐membership approaches
In this paper, the problem of identification for passive robust fault detection, when a
bounded description of the modelling uncertainty is considered, is addressed. Two set‐membership …
bounded description of the modelling uncertainty is considered, is addressed. Two set‐membership …
[HTML][HTML] Attack isolation and location for a complex network cyber-physical system via zonotope theory
X Zhang, F Zhu, J Zhang, T Liu - Neurocomputing, 2022 - Elsevier
This paper investigates the attack isolation (AI) and attack location (AL) problems for a cyber-physical
system (CPS) based on the combination of the H-infinity observer and the …
system (CPS) based on the combination of the H-infinity observer and the …
Zonotopes and the LP-Newton method
S Fujishige, T Hayashi, K Yamashita… - Optimization and …, 2009 - Springer
… Linear programming problems can be formulated in terms of a zonotope, a kind of greedy …
for linear programming that is based on the zonotope formulation and the minimum-norm-point …
for linear programming that is based on the zonotope formulation and the minimum-norm-point …
The cd-index of zonotopes and arrangements
LJ Billera, R Ehrenborg, M Readdy - Mathematical essays in honor of Gian …, 1998 - Springer
… special class of polytopes, the zonotopes, and show for these that there is no reduction
whatsoever; that is, we show that the flag f-vectors of zonotopes satisfy only the affine relations …
whatsoever; that is, we show that the flag f-vectors of zonotopes satisfy only the affine relations …