Projection methods for finding the greatest element of the intersection of max-closed convex sets
Sign Up to like & getrecommendations! Published in 2024 at "Annals of Operations Research"
DOI: 10.1007/s10479-024-05980-z
Abstract: We focus on the problem of finding the greatest element of the intersection of max-closed convex sets. For this purpose, we analyze the famous method of cyclic projections and show that, if this method is… read more here.
Keywords: convex sets; element intersection; closed convex; greatest element ... See more keywords
Weak⁎ derived sets of convex sets in duals of non-reflexive spaces
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2021.109259
Abstract: We investigate weak∗ derived sets, that is the sets of weak∗ limits of bounded nets, of convex subsets of duals of non-reflexive Banach spaces and their possible iterations. We prove that a dual space of… read more here.
Keywords: non reflexive; duals non; sets convex; derived sets ... See more keywords
On the Cheeger inequality for convex sets
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125443
Abstract: Abstract In this paper, we prove new sharp bounds for the Cheeger constant of planar convex sets that we use to study the relations between the Cheeger constant and the first eigenvalue of the Laplace… read more here.
Keywords: convex sets; planar convex; new sharp; cheeger inequality ... See more keywords
Characterization of AE solution sets of parametric linear systems based on the techniques of convex sets
Sign Up to like & getrecommendations! Published in 2017 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2017.07.035
Abstract: Abstract New approach to linear systems with uncertain parameters is proposed. The notion of AE solution sets is extended to the case when the domain of parameters need not be an interval vector. The tools… read more here.
Keywords: sets parametric; characterization solution; solution; convex sets ... See more keywords
Inequalities for the Radon Transform on Convex Sets
Sign Up to like & getrecommendations! Published in 2021 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rnab122
Abstract: Several years ago the authors started looking at some problems of convex geometry from a more general point of view, replacing volume by an arbitrary measure. This approach led to new general properties of the… read more here.
Keywords: convex sets; inequalities radon; transform convex; geometry ... See more keywords
A Minimax Model for Generalized Penetration Distance Between Convex Sets by Directed Hausdorff Distance
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Robotics and Automation Letters"
DOI: 10.1109/lra.2022.3166111
Abstract: The penetration distance, which characterizes the depth of intersection between two sets, is a fundamental computational geometry problem with a wide variety of applications in image processing, robotics, and circuit design. However, the penetration distance… read more here.
Keywords: convex sets; generalized penetration; distance; penetration distance ... See more keywords
Planning Shorter Paths in Graphs of Convex Sets by Undistorting Parametrized Configuration Spaces
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Robotics and Automation Letters"
DOI: 10.1109/lra.2025.3564204
Abstract: Optimization based motion planning provides a useful modeling framework through various costs and constraints. Using Graph of Convex Sets (GCS) for trajectory optimization gives guarantees of feasibility and optimality by representing configuration space as the… read more here.
Keywords: shorter paths; convex sets; configuration; graphs convex ... See more keywords
DrPOCS: Drug Repositioning Based on Projection Onto Convex Sets
Sign Up to like & getrecommendations! Published in 2019 at "IEEE/ACM Transactions on Computational Biology and Bioinformatics"
DOI: 10.1109/tcbb.2018.2830384
Abstract: Drug repositioning, i.e., identifying new indications for known drugs, has attracted a lot of attentions recently and is becoming an effective strategy in drug development. In literature, several computational approaches have been proposed to identify… read more here.
Keywords: convex sets; drug; based projection; onto convex ... See more keywords
An Efficient Unified Algorithm for the Minimum Euclidean Distance Between Two Collections of Compact Convex Sets
Sign Up to like & getrecommendations! Published in 2025 at "IEEE Transactions on Robotics"
DOI: 10.1109/tro.2025.3562478
Abstract: In this article, we present an efficient unified algorithm for the minimum Euclidean distance between two collections of compact convex sets, each of which can be a collection of convex primitives, such as ellipsoids, capsules,… read more here.
Keywords: euclidean distance; distance; convex sets; distance two ... See more keywords
Some fixed point theorems on non-convex sets
Sign Up to like & getrecommendations! Published in 2017 at "Applied general topology"
DOI: 10.4995/agt.2017.7452
Abstract: In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$ , $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if… read more here.
Keywords: theorems non; point; non convex; point theorems ... See more keywords