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

Кафедра математической теории моделирования систем управления

Research output › › 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
Publication status	Published - 10 Jul 2017
Event	2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017: dedicated to the Memory of V.F. Demyanov - Saint-Petersburg Duration: 21 May 2017 → 26 May 2017 http://www.pdmi.ras.ru/EIMI/2017/CNSA/

Conference

Conference	2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017
Abbreviated title	CNSA 2017
Country	Russian Federation
City	Saint-Petersburg
Period	21/05/17 → 26/05/17
Internet address	http://www.pdmi.ras.ru/EIMI/2017/CNSA/

Scopus subject areas

Modelling and Simulation
Analysis
Applied Mathematics
Control and Optimization

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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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note = "2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 : dedicated to the Memory of V.F. Demyanov, CNSA 2017 ; Conference date: 21-05-2017 Through 26-05-2017",

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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 (Dedicated to the Memory of V.F. Demyanov), CNSA 2017, Saint-Petersburg, 21/05/17. https://doi.org/10.1109/CNSA.2017.7974006

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N2 - 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.

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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