A direct approach to the finite element solution of elliptic optimal control problems

A general framework is developed for the finite element solution of optimal control problems governed by elliptic nonlinear partial differential equat ions. Typical applications are steady-state problems in nonlinear continuum mechanics, where a certain property of the solution (a function of displac ements, temperatures, etc.) is to be minimized by applying control loads. i n contrast to existing formulations, which are based on the "adjoint state, " the present formulation is a direct one, which does not use adjoint varia bles. The formulation is presented first in a general nonlinear setting, th en specialized to a case leading to a sequence of quadratic programming pro blems, and then specialized further to the unconstrained case. Linear gover ning partial differential equations are also considered as a special case i n each of these categories. (C) 1999 John Wiley & Sons, Inc.