Delfour, Michel C.; Zolésio, Jean-Paul Velocity method and Lagrangian formulation for the computation of the shape Hessian. (English) Zbl 0747.49007 SIAM J. Control Optimization 29, No. 6, 1414-1442 (1991). The authors study the shape Hessian of a shape functional by the velocity method. A shape functional is a function defined on a suitable class of subsets of \(\mathbb{R}^ n\) and the shape Hessian is the second derivative of this function as the domain is perturbed via a smooth non-degenerate vector field. The properties of the shape Hessian are used to examine various optimization problems in which the domain varies. Reviewer: G.M.Lieberman (Ames) Cited in 26 Documents MSC: 49J20 Existence theories for optimal control problems involving partial differential equations Keywords:shape Hessian of a shape functional; velocity method; smooth non- degenerate vector field PDFBibTeX XMLCite \textit{M. C. Delfour} and \textit{J.-P. Zolésio}, SIAM J. Control Optim. 29, No. 6, 1414--1442 (1991; Zbl 0747.49007) Full Text: DOI