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

• Published in: Applied mathematics and mechanics Vol. 32; no. 1; pp. 107 - 118
• Main Authors: Chen, Xi, Yao, Yi-rong, Zheng, Quan
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.01.2011; Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, P.R.China%Department of Mathematics, College of Science, Shanghai University, Shanghai 200444, P.R.China; Department of Mathematics, Columbus State University, Columbus, GA 31907, USA
• Subjects: Algorithms; Applications of Mathematics; Approximation; Classical Mechanics; Constraints; Convergence; Deviation; Fluid- and Aerodynamics; Integrals; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Partial Differential Equations; R-convergence; 58K30; variable measure; O224; deviation integral; 90C26; global optimization; finite-dimensional approximation; 41A29
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-011-1398-8

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.