Nonlinear Programs with Unbounded Lagrange Multiplier Sets

We investigate nonlinear programs that have a nonempty but possibly unbounded Lagrange multiplier set and that satisfy the quadraticgrowth condition. We show that such programs can be transformed, by relaxing the constraints and adding a linear penalty term to the objective function, into equivalent nonlinear programs that have diierentiable data and a bounded Lagrange multiplier set and that satisfy the quadratic growth condition. As a result we can deene, for this type of problem, algorithms that are linearly convergent, using only rst-order information, and superlinearly convergent.