Composite Nonsmooth Programming with Gâteaux Differentiability
V. Jeyakumar · SIAM Journal on Optimization · 1991
This paper examines constrained nonsmooth optimization problems where the objective function and the constraints are compositions of locally Lipschitz functions and Gâteaux differentiable functions, but are not necessarily Fréchet differentiable or strict differentiable. Lagrangian necessary and sufficient optimality conditions are presented for various classes of composite programs. These are obtained by constructing appropriate convex approximations for composite functions. The Lagrange multipliers are also characterized in terms of subgradients of the value function under appropriate conditions.