The author studies the following abstract control problem: minimize J(u) subject to \(| u(t)| \leq 1\), a.e. on [0,T] where \(S: L^ 2(0,T)\to L^ 2(I)\) is a linear, compact operator, while \(I\subset {\mathbb{R}}^ m\) smooth compact manifold and \(J: L^ 2(I)\to {\mathbb{R}}\) is Fréchet-differentiable.
Generally speaking, a number of control problems arising in boundary control of heat conduction is subsumed under this abstract setting. The algorithm employed consists, basically, of two steps: The first step computes the number and approximate locations of the switching points and the second step takes the switching points as variables and utilises a Newton-type method to compute their exact locations.