Convex Cones and Conjugacy for Inequality Control Constraints

Three approaches to conjugacy available in the literature, applicable to optimal control problems with inequality and equality constraints in the control, are studied. A clear and unified review of the second order conditions obtained in each case is given, and the three definitions of "generalized conjugate points" are improved in the sense that, either the range of applicability is enlarged, or the conditions defining membership of the different sets of points are simplified.