Optimization on fractals and stability

M. Barnsley; U. Freiberg; D. La Torre

Optimization on fractals and stability

M. Barnsley, U. Freiberg, D. La Torre

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

1 Citation (Scopus)

Abstract

We study the stability of variational problems involving sequences of sets and measures generated by iterated function systems and approaching a fractal object in Hausdorff and Monge-Kantorovich metric, respectively. We give some results concerning the convergence of the corresponding minimizers.

Original language	English
Pages (from-to)	695-708
Number of pages	14
Journal	Journal of Nonlinear and Convex Analysis
Volume	13
Issue number	4
Publication status	Published - Oct 2012

Cite this

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title = "Optimization on fractals and stability",

abstract = "We study the stability of variational problems involving sequences of sets and measures generated by iterated function systems and approaching a fractal object in Hausdorff and Monge-Kantorovich metric, respectively. We give some results concerning the convergence of the corresponding minimizers.",

keywords = "Fractal, Hausdorff distance, Iterated function system, Monge-Kantorovich distance, Self-similar measure, Self-similar set, V-variable fractal, Variational problem",

author = "M. Barnsley and U. Freiberg and {La Torre}, D.",

year = "2012",

month = oct,

language = "English",

volume = "13",

pages = "695--708",

journal = "Journal of Nonlinear and Convex Analysis",

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T1 - Optimization on fractals and stability

AU - Barnsley, M.

AU - Freiberg, U.

AU - La Torre, D.

PY - 2012/10

Y1 - 2012/10

N2 - We study the stability of variational problems involving sequences of sets and measures generated by iterated function systems and approaching a fractal object in Hausdorff and Monge-Kantorovich metric, respectively. We give some results concerning the convergence of the corresponding minimizers.

AB - We study the stability of variational problems involving sequences of sets and measures generated by iterated function systems and approaching a fractal object in Hausdorff and Monge-Kantorovich metric, respectively. We give some results concerning the convergence of the corresponding minimizers.

KW - Fractal

KW - Hausdorff distance

KW - Iterated function system

KW - Monge-Kantorovich distance

KW - Self-similar measure

KW - Self-similar set

KW - V-variable fractal

KW - Variational problem

UR - http://www.scopus.com/inward/record.url?scp=84894228040&partnerID=8YFLogxK

M3 - Article

SN - 1345-4773

VL - 13

SP - 695

EP - 708

JO - Journal of Nonlinear and Convex Analysis

JF - Journal of Nonlinear and Convex Analysis

IS - 4

ER -

Optimization on fractals and stability

Abstract

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