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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (1): 107-118.doi: https://doi.org/10.1007/s10483-011-1398-8

• Articles • 上一篇    下一篇

Finite-dimensional approximation to global minimizers in functional spaces with R-convergence

陈熙1 姚奕荣1 郑权1,2   

  1. 1. Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, P. R. China;
    2. Department of Mathematics, Columbus State University, Columbus, GA 31907, USA
  • 收稿日期:2010-09-24 修回日期:2010-11-24 出版日期:2011-01-10 发布日期:2011-01-01

Finite-dimensional approximation to global minimizers in functional spaces with R-convergence

CHEN Xi1, YAO Yi-Rong1, ZHENG Quan1,2   

  1. 1. Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, P. R. China;
    2. Department of Mathematics, Columbus State University, Columbus, GA 31907, USA
  • Received:2010-09-24 Revised:2010-11-24 Online:2011-01-10 Published:2011-01-01

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摘要： A new concept of convergence (R-convergence) of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.

Abstract: A new concept of convergence (R-convergence) of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.

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