Numerical optimization for the calculus of variations by gradients on non-Hilbert Sobolev spaces using conjugate gradients and normalized differential equations of steepest descent

• Published in: Nonlinear analysis Vol. 71; no. 12; pp. e665 - e671
• Main Author: Stein, Ivie
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.12.2009
• Subjects: Calculus of variations; Conjugate gradients; Descent; Differential equations; Mathematical analysis; Mathematical models; Minimization; Norms; Numerical optimization; Optimization; Steepest descent; Conjugate gradients; Numerical optimization; Steepest descent; Calculus of variations

The purpose of this paper is to illustrate the application of numerical optimization methods for nonquadratic functionals defined on non-Hilbert Sobolev spaces. These methods use a gradient defined on a norm-reflexive and hence strictly convex normed linear space. This gradient is defined by Michael...