Premium
A direct approach to the finite element solution of elliptic optimal control problems
Author(s) -
Givoli Dan
Publication year - 1999
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199905)15:3<371::aid-num7>3.0.co;2-x
Subject(s) - mathematics , partial differential equation , finite element method , nonlinear system , elliptic partial differential equation , partial derivative , optimal control , mathematical analysis , mathematical optimization , physics , quantum mechanics , thermodynamics
A general framework is developed for the finite element solution of optimal control problems governed by elliptic nonlinear partial differential equations. Typical applications are steady‐state problems in nonlinear continuum mechanics, where a certain property of the solution (a function of displacements, temperatures, etc.) is to be minimized by applying control loads. In contrast to existing formulations, which are based on the “adjoint state,” the present formulation is a direct one, which does not use adjoint variables. The formulation is presented first in a general nonlinear setting, then specialized to a case leading to a sequence of quadratic programming problems, and then specialized further to the unconstrained case. Linear governing partial differential equations are also considered as a special case in each of these categories. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15:371–388, 1999