Optimal processes governed by integral equations (Q1085428)

The author considers the problem of minimizing the functional \(\int^{1}_{0}f^ 0(\phi (t),u(t),t)dt\) subject to \[ \phi (t)=f(t)+\int^{t}_{0}L(t,\phi (s),u(s),s)ds,\quad \int^{1}_{0}M(\phi (t),u(t),t)dt+W(\phi (1))=0. \] The author derives optimality conditions using relaxed controls. In the special case where the control set is a convex polyhedron it is shown, from a pointwise minimum principle derived, that the control takes values in the vertices of the polyhedron.