Known SSC Results for the Continuous Problems

No attempt will be made to quote all relevant results on optimality conditions. In the case of problem (P) the following set of SSC is stated in [1]. First, the Lagrange function

is defined with the Lagrange multiplier function . Then the second derivative of with respect to is called and is evaluated at a point satisfying the first order optimality conditions. The key requirement is the inequality

SSC have not been stated exactly for the two elliptic control problems (EB),
(ED) in the previous section, but a series of papers address special cases.
In [4], for example, a good overview of the literature is given
and the boundary control problem covered in much technical detail is nearly
identical to (EB) except for

On the other hand, a problem of type (ED) but with

and the tracking type objective function (2.3) is extensively analyzed in [2]. Finally, the state-constrained case is addressed in [5] for (EB) and in [20] for (P).

2001-06-17