For both differentiable and nondifferentiable functions defined in abstract spaces we characterize the generalized convex property, here called cone-invexity, in terms of Lagrange multipliers. Several classes of such functions are given. In addition an extended Kuhn-Tucker type optimality condition and a duality result are obtained for quasidifferentiable programming problems.

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For sublinear mappings between normed linear spaces a generalization of Farkas' lemma is established thus extending the known results to include a class of nonqinear functions. A generalized Motzkin alternative theorem is established and as an application we provide a Kuhn-Tucker type necessary optimality condition for a non-differentiable mathematical programming problem.

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