ISSN:
1573-2878
Keywords:
Integrals of multivalued mappings
;
linear optimal control
;
attainable set
;
convexity
;
constrained optimization
;
conditional gradient method
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Using the notion of the local convexity index, we characterize in a quantitative way the local convexity of a set in then-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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00940201
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