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

Finite-dimensional approximation to global minimizers in functional spaces with R-convergence
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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. 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.
作者 陈熙 姚奕荣 郑权
机构地区 Department of Mathematics Department of Mathematics
出处 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第1期107-118,共12页 应用数学和力学（英文版）
基金 Project supported by the National Natural Science Foundation of China(No.11071158) Shanghai Leading Academic Discipline Project(No.S30104)
关键词 global optimization deviation integral variable measure R-convergence finite-dimensional approximation ／ global optimization, deviation integral, variable measure, R-convergence,finite-dimensional approximation ／
分类号 O174.41 [理学—基础数学]
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Applied Mathematics and Mechanics(English Edition)
2011年 第1期

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