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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Ward, D., Lee, G. Upper Subderivatives and Generalized Gradients of the Marginal Function of a Non-Lipschitzian Program. Annals of Operations Research 101, 299–312 (2001). https://doi.org/10.1023/A:1010953431290
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DOI: https://doi.org/10.1023/A:1010953431290