Necessary conditions for optimality for paths lying on a corner

A class of optimization problems is investigated in which some of the functions, continuous in all their arguments, have continuous right and left hand derivatives but are not equal at a point called the corner. For this nonclassical problem, a set of first order necessary conditions for stationarity is determined for an optimal path which may have arcs lying on a corner for a nonzero length of time. Enough conditions are provided to constuct an extremal path. This, in part, is achieved by noting that the corner defines a manifold in which the derivatives of all the functions are uniquely defined. Two examples, representing possible aggregate production and employment planning models, illustrate the theory.