Finite Dimensional Approximation to Global Minimizers in Functional Spaces With <em>R</em>-Convergence

CHEN Xi; YAO Yi-rong; ZHENG Quan

doi:10.3879/j.issn.1000-0887.2011.01.011

Volume 32 Issue 1

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CHEN Xi, YAO Yi-rong, ZHENG Quan. Finite Dimensional Approximation to Global Minimizers in Functional Spaces With R-Convergence[J]. Applied Mathematics and Mechanics, 2011, 32(1): 103-112. doi: 10.3879/j.issn.1000-0887.2011.01.011

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Finite Dimensional Approximation to Global Minimizers in Functional Spaces With R-Convergence

doi: 10.3879/j.issn.1000-0887.2011.01.011

1.
Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;

Received Date: 2010-09-20
Rev Recd Date: 2010-11-24
Publish Date: 2011-01-15

Abstract

Abstract

New concept of convergence(R-convergence)of a sequence of measures was applied to characterize global minimizers in functional space as a sequence of approximating solutions in finite-dimensional spaces.A deviation integral approach was used to find such solutions.For a constrained problem,a penalized deviation integral algorithm was proposed to convert it to unconstrained ones.A numerical example on optimal control problem with non convex state constrains was given to show that the algorithm is efficient.
- global optimization,
- deviation integral,
- variable measure,
- R-convergence,
- finite dimensional approximation

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References(12)

References

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