From continuous to discrete

Carlile Lavor; Leo Liberti; Weldon A. Lodwick; Tiago Mendonça da Costa

doi:10.1007/978-3-319-57183-6_3

From continuous to discrete

Carlile Lavor
, Leo Liberti
, Weldon A. Lodwick
, Tiago Mendonça da Costa

University of Campinas (UNICAMP)
University of Colorado at Denver

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Chapitre › Revue par des pairs

Résumé

One approach that has been used to solve the DGP is to represent it as a continuous optimization problem [59]. To understand it, we consider a DGP with K = 2, V = {u, v, s}, E = {{ u, v}, {v, s}}, where the associated quadratic system is [Formula presented] which can be rewritten as [Formula presented] Consider the function f: ℝ⁶→ ℝ, defined by [Formula presented] It is not hard to realize that the solution x^∗∈ ℝ⁶ of the associated DGP can be found by solving the following problem: [Formula presented] That is, we wish to find the point x*∈ ℝ⁶ which attains the smallest value of f.

langue originale	Anglais
titre	SpringerBriefs in Computer Science
Editeur	Springer
Pages	13-20
Nombre de pages	8
Edition	9783319571829
Les DOIs	https://doi.org/10.1007/978-3-319-57183-6_3
état	Publié - 1 janv. 2017

Série de publications

Nom	SpringerBriefs in Computer Science
nombre	9783319571829
Volume	0
ISSN (imprimé)	2191-5768
ISSN (Electronique)	2191-5776

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10.1007/978-3-319-57183-6_3

Contient cette citation

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title = "From continuous to discrete",

abstract = "One approach that has been used to solve the DGP is to represent it as a continuous optimization problem [59]. To understand it, we consider a DGP with K = 2, V = \{u, v, s\}, E = \{\{ u, v\}, \{v, s\}\}, where the associated quadratic system is [Formula presented] which can be rewritten as [Formula presented] Consider the function f: ℝ6→ ℝ, defined by [Formula presented] It is not hard to realize that the solution x∗∈ ℝ6 of the associated DGP can be found by solving the following problem: [Formula presented] That is, we wish to find the point x*∈ ℝ6 which attains the smallest value of f.",

author = "Carlile Lavor and Leo Liberti and Lodwick, \{Weldon A.\} and \{Mendon{\c c}a da Costa\}, Tiago",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2017.",

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AU - Lavor, Carlile

AU - Liberti, Leo

AU - Lodwick, Weldon A.

AU - Mendonça da Costa, Tiago

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N2 - One approach that has been used to solve the DGP is to represent it as a continuous optimization problem [59]. To understand it, we consider a DGP with K = 2, V = {u, v, s}, E = {{ u, v}, {v, s}}, where the associated quadratic system is [Formula presented] which can be rewritten as [Formula presented] Consider the function f: ℝ6→ ℝ, defined by [Formula presented] It is not hard to realize that the solution x∗∈ ℝ6 of the associated DGP can be found by solving the following problem: [Formula presented] That is, we wish to find the point x*∈ ℝ6 which attains the smallest value of f.

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From continuous to discrete

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