Differences of Convex Compact Sets in the Space of Directed Sets. Part II: Visualization of Directed Sets

Robert Baier; Elza M. Farkhi

doi:10.1023/A:1012009529492

Differences of Convex Compact Sets in the Space of Directed Sets. Part II: Visualization of Directed Sets

Robert Baier^*, Elza M. Farkhi

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is a continuation of the author's first paper (Set-Valued Anal. 9 (2001), pp. 217-245), where the normed and partially ordered vector space of directed sets is constructed and the cone of all nonempty convex compact sets in ℝⁿ is embedded. A visualization of directed sets and of differences of convex compact sets is presented and its geometrical components and properties are studied. The three components of the visualization are compared with other known differences of convex compact sets.

Original language	English
Pages (from-to)	247-272
Number of pages	26
Journal	Set-Valued Analysis
Volume	9
Issue number	3
DOIs	https://doi.org/10.1023/A:1012009529492
State	Published - 2001

Keywords

Convex analysis
Differences of convex sets and their visualization
Directed intervals
Directed sets
Interval analysis

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title = "Differences of Convex Compact Sets in the Space of Directed Sets. Part II: Visualization of Directed Sets",

abstract = "This paper is a continuation of the author's first paper (Set-Valued Anal. 9 (2001), pp. 217-245), where the normed and partially ordered vector space of directed sets is constructed and the cone of all nonempty convex compact sets in ℝn is embedded. A visualization of directed sets and of differences of convex compact sets is presented and its geometrical components and properties are studied. The three components of the visualization are compared with other known differences of convex compact sets.",

keywords = "Convex analysis, Differences of convex sets and their visualization, Directed intervals, Directed sets, Interval analysis",

author = "Robert Baier and Farkhi, {Elza M.}",

note = "Funding Information: ★ Partially supported by The Hermann Minkowski Center for Geometry at Tel Aviv University, Israel.",

year = "2001",

doi = "10.1023/A:1012009529492",

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AU - Farkhi, Elza M.

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PY - 2001

Y1 - 2001

N2 - This paper is a continuation of the author's first paper (Set-Valued Anal. 9 (2001), pp. 217-245), where the normed and partially ordered vector space of directed sets is constructed and the cone of all nonempty convex compact sets in ℝn is embedded. A visualization of directed sets and of differences of convex compact sets is presented and its geometrical components and properties are studied. The three components of the visualization are compared with other known differences of convex compact sets.

AB - This paper is a continuation of the author's first paper (Set-Valued Anal. 9 (2001), pp. 217-245), where the normed and partially ordered vector space of directed sets is constructed and the cone of all nonempty convex compact sets in ℝn is embedded. A visualization of directed sets and of differences of convex compact sets is presented and its geometrical components and properties are studied. The three components of the visualization are compared with other known differences of convex compact sets.

KW - Convex analysis

KW - Differences of convex sets and their visualization

KW - Directed intervals

KW - Directed sets

KW - Interval analysis

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JO - Set-Valued and Variational Analysis

JF - Set-Valued and Variational Analysis

IS - 3

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Differences of Convex Compact Sets in the Space of Directed Sets. Part II: Visualization of Directed Sets

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Keywords

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