Saddlepoint optimality conditions are derived for a class of nondifferentiable programming problems of the form minf(r) subject to x∈A,g(x)∈B, where A⊆X, a Banach space, and B⊆V, an order complete vector lattice. To establish many of the results the functions delimiting the problem are assumed to be order-Lipschitz, a property which is shown to be related to other Lipschitz-type definitions in the literature. A nonsmooth analysis for order-Lipschitz functions is included; in particular, directional derivatives, generalized gradients, optimality conditions and results concerning a calculus of generalized gradients are discussed. The saddlepoint optimality conditions are shown to compare favorably with other optimality conditions in the literature.
