, F. Guillén
and M. A.
Control and Partial Differential Equations
In this work, some type of optimal control problems with equality
constraints given by Partial Differential Equations (PDE) and convex
inequality constraints are considered, obtaining their
corresponding first order necessary optimality conditions by means of
Dubovitskii-Milyutin (DM) method. Firstly, we consider problems with
one objective functional (or scalar problems) but non-well posed
equality constraints, where existence and uniqueness of state in
function on control is not true (either one has existence but not
uniqueness of state, or one has not existence of state for any
control). In both cases, the classical Lions argument (re-writing the
problem as an optimal control problem for the control without equality
constraints, see for instance ) can not be applied.
Afterwards, we consider multiobjective problems (or vectorial
problems), considering three different concepts of solution: Pareto,
Nash and Stackelberg. In all cases, an adequate abstract DM method is
developed followed by an example.
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October 07, 2004
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