Shape Differentiability of Lagrangians and Application to Stokes Problem

Shape Differentiability of Lagrangians and Application to Stokes Problem Full article

Journal

SIAM Journal on Control and Optimization
ISSN: 0363-0129

Output data

Year: 2018, Volume: 56, Number: 5, Pages: 3668-3684 Pages count : 17 DOI: 10.1137/17m1125327

Tags

Constrained minimization; Lagrangian; Primal and dual cone; Primal-dual minimax problem; Shape derivative; Stokes problem; Velocity method

Authors

Kovtunenko V.A. ^1,2 , Ohtsuka Kohji ³

Affiliations

1	Institute for Mathematics and Scientific Computing, Karl-Franzens University of Graz
2	Lavrent’ev Institute of Hydrodynamics, Siberian Division of Russian Academy of Sciences
3	Faculty of Information Design and Sociology, Hiroshima Kokusai Gakuin University

A class of convex constrained minimization problems over polyhedral cones for geometry-dependent quadratic objective functions is considered in a functional analysis framework. Shape differentiability of the primal minimization problem needs a bijective property for mapping of the primal cone. This restrictive assumption is relaxed to bijection of the dual cone within the Lagrangian formulation as a primal-dual minimax problem. In this paper, we give results on primal-dual shape sensitivity analysis that extends the class of shape-differentiable problems supported by an explicit formula of the shape derivative. We apply the results to the Stokes problem under mixed Dirichlet—Neumann boundary conditions subject to the divergence-free constraint.

Kovtunenko V.A. , Ohtsuka K.
Shape Differentiability of Lagrangians and Application to Stokes Problem
SIAM Journal on Control and Optimization. 2018. V.56. N5. P.3668-3684. DOI: 10.1137/17m1125327 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000448810200022
Scopus:	2-s2.0-85056107876
Elibrary:	37218135
OpenAlex:	W2886977095

DB	Citing
Scopus	14
OpenAlex	16
Elibrary	15
Web of science	13