Differential stability in infinite-dimensional nonlinear programming

F. Lempio, H. Maurer: Differential stability in infinite-dimensional nonlinear programming
Applied Mathematics and Optimization 6 (2), 139 - 152, 1980

DOI: 10.1007/BF01442889
MR Nummer: 563531
Zentralblattnummer: 0426.90072
Keywords: differential stability; infinite-dimensional nonlinear programming; differentiable perturbations in the objective function; necessary and sufficient conditions; existence of the directional derivative; differential perturbations in the constraints
Mathematics Subject Classification Code: 90C48 (90C30 90C31 93D99)


Abstract:

In this paper stability properties of the extremal value function are studied for infinite-dimensional nonlinear optimization problems with differentiable perturbations in the objective function and in the constraints. In particular, upper and lower bounds for the directional derivative of the extremal value function as well as necessary and sufficient conditions for the existence of the directional derivative are given.

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