About constructing a dual polyhedral cone in R3

Lyudmila Polyakova; Marina Popova; Vladimir Karelin

doi:10.1109/CNSA.2017.7974006

About constructing a dual polyhedral cone in R³

Lyudmila Polyakova, Marina Popova, Vladimir Karelin

Department of Mathematical Modelling of Control Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The problem of constructing a dual cone of a convex polyhedral cone arises in many mathematical and applied researches. In the paper the method of constructing the dual cone to the acute convex polyhedral cone in R³ is proposed. The Householder transformation, creating a convex hull on the plane and projecting the point lying on the z-axis onto a corresponding face are the basic operations which we used.

Original language	English
Title of host publication	2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings
Editors	L. N. Polyakova
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781509062607
DOIs	https://doi.org/10.1109/CNSA.2017.7974006
State	Published - 10 Jul 2017
Event	2017 Constructive Nonsmooth Analysis and Related Topics: dedicated to the Memory of V.F. Demyanov - Saint-Petersburg, Russian Federation Duration: 22 May 2017 → 27 May 2017 http://www.mathnet.ru/php/conference.phtml?confid=968&option_lang=rus http://www.pdmi.ras.ru/EIMI/2017/CNSA/

Conference

Conference	2017 Constructive Nonsmooth Analysis and Related Topics
Abbreviated title	CNSA 2017
Country/Territory	Russian Federation
City	Saint-Petersburg
Period	22/05/17 → 27/05/17
Internet address	http://www.mathnet.ru/php/conference.phtml?confid=968&option_lang=rus http://www.pdmi.ras.ru/EIMI/2017/CNSA/

Scopus subject areas

Modelling and Simulation
Analysis
Applied Mathematics
Control and Optimization

Access to Document

10.1109/CNSA.2017.7974006

Cite this

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title = "About constructing a dual polyhedral cone in R3",

abstract = "The problem of constructing a dual cone of a convex polyhedral cone arises in many mathematical and applied researches. In the paper the method of constructing the dual cone to the acute convex polyhedral cone in R3 is proposed. The Householder transformation, creating a convex hull on the plane and projecting the point lying on the z-axis onto a corresponding face are the basic operations which we used.",

author = "Lyudmila Polyakova and Marina Popova and Vladimir Karelin",

year = "2017",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

address = "United States",

note = "2017 Constructive Nonsmooth Analysis and Related Topics : dedicated to the Memory of V.F. Demyanov, CNSA 2017 ; Conference date: 22-05-2017 Through 27-05-2017",

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Polyakova, L, Popova, M & Karelin, V 2017, About constructing a dual polyhedral cone in R³. in LN Polyakova (ed.), 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings., 7974006, Institute of Electrical and Electronics Engineers Inc., 2017 Constructive Nonsmooth Analysis and Related Topics, Saint-Petersburg, Russian Federation, 22/05/17. https://doi.org/10.1109/CNSA.2017.7974006

About constructing a dual polyhedral cone in R³. / Polyakova, Lyudmila; Popova, Marina; Karelin, Vladimir.

2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings. ed. / L. N. Polyakova. Institute of Electrical and Electronics Engineers Inc., 2017. 7974006.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The problem of constructing a dual cone of a convex polyhedral cone arises in many mathematical and applied researches. In the paper the method of constructing the dual cone to the acute convex polyhedral cone in R3 is proposed. The Householder transformation, creating a convex hull on the plane and projecting the point lying on the z-axis onto a corresponding face are the basic operations which we used.

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