Upper Subderivatives and Generalized Gradients of the Marginal Function of a Non-Lipschitzian Program

D.E. Ward and G.M. Lee

Annals of Operations Research, 2001, vol. 101, issue 1, 299-312

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. Copyright Kluwer Academic Publishers 2001

Keywords: parametric optimization problem; marginal function; upper subderivative; generalized subdifferential; singular approximate subdifferential; Clarke tangent cone; normal cones (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1010953431290

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