Optimization with generalized invexity

Constrained optimization is studied, with nonsmooth (Lipschitz) functions in abstract spaces and cone-constraints. Some more general Lagrangian necessary conditions are obtained, using strict minimum and approximation methods. These conditions are sufficient for a minimum under generalized invex assumptions. A characterization is obtained for generalized invexity, generalizing a known result for differentiable functions. Generalized invexity happens exactly when the generalized Wolfe and Lagrangian dual problems coincide.