Journal of Optimization Theory and Applications

, Volume 70, Issue 3, pp 443–466 | Cite as

Local stability of solutions to differentiable optimization problems in banach spaces

Contributed Papers

Abstract

This paper considers a class of nonlinear differentiable optimization problems depending on a parameter. We show that, if constraint regularity, a second-order sufficient optimality condition, and a stability condition for the Lagrange multipliers hold, then for sufficiently smooth perturbations of the constraints and the objective function the optimal solutions locally obey a type of Lipschitz condition. The results are applied to finite-dimensional problems, equality constrained problems, and optimal control problems.

Key Words

Nonlinear optimization parametric programming stability of solutions optimal control 

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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • W. Alt
    • 1
  1. 1.Mathematisches InstitutUniversität BayreuthBayreuthGermany

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