Upper subderivatives and generalized gradients of the marginal function of a non-Lipschitzian program

Upper subderivatives and generalized gradients of the marginal function of a non-Lipschitzian program

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Article ID: iaor20021387
Country: Netherlands
Volume: 101
Issue: 1
Start Page Number: 299
End Page Number: 312
Publication Date: Jan 2001
Journal: Annals of Operations Research
Authors: ,
Abstract:

We obtain an upper bound for the upper subderivative of the marginal function of an abstract parametric optimization problem when the objective function is lower semicontinuous. Moreover, we apply the result to a nonlinear program with right-hand side perturbations. As a result, we obtain an upper bound for the upper subderivative of the marginal function of a nonlinear program with right-hand side perturbations, which is expressed in ‘dual form’ in terms of appropriate Lagrange multipliers. Finally, we present conditions which imply that the marginal function is locally Lipschitzian.

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