On the convexity of integrals of multivalued mappings. Applications in control theory
type: Item
instance of: scholarly article
title: On the convexity of integrals of multivalued mappings. Applications in control theory
zbMATH Open document ID: 0596.49011
DOI: 10.1007/BF00940201
published in: Journal of Optimization Theory and Applications
publication date: 1987-01-01T00:00:00Z
review text: Using the notion of the local convexity index, we characterize in a quantitative way the local convexity of a set in the n-dimensional Euclidean space, defined by an integral of a multivalued mapping. We estimate the rate of convergence of the conditional gradient method for solving an abstract optimization problem by means of the convexity index of the constraining set at the solution point. These results are applied to the qualitative analysis of the solutions of time-optimal and Mayer problems for linear control systems, as well as for estimating the convergence rate of algorithms solving these problems.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 90C52
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 3960383
zbMATH Keywords: local convexity index
zbMATH Keywords: integral of a multivalued mapping
zbMATH Keywords: rate of convergence
zbMATH Keywords: conditional gradient method
zbMATH Keywords: time-optimal and Mayer problems
author: Vladimir M. Veliov
MaRDI profile type: Publication
Wikidata QID: Q58296927
cites work: Integrals of set-valued functions
cites work: An Iterative Procedure for Computing the Minimum of a Quadratic Form on a Convex Set
cites work: Q5576518
cites work: A Tight Upper Bound on the Rate of Convergence of Frank-Wolfe Algorithm
full work available at URL: https://doi.org/10.1007/bf00940201
OpenAlex ID: W1970824477
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description: scientific article; zbMATH DE number 3960383