Nonlinear Programs with Unbounded Lagrange Multiplier Sets

TitleNonlinear Programs with Unbounded Lagrange Multiplier Sets
Publication TypeReport
Year of Publication2000
AuthorsAnitescu, M
Date Published10/2000
Other NumbersANL/MCS-P793-0200
Abstract

We investigate nonlinear programs that have a nonempty but possibly unbounded Lagrange multiplier set and that satisfy the quadratic growth 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 differentiable data and a bounded Lagrange multiplier set and that satisfy the quadratic growth condition. As a result we can define, for this type of problem, algorithms that are linearly convergent, using only first-order information, and superlinearly convergent.

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