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Local stability of solutions to differentiable optimization problems in banach spaces (1991)

Alt, W.

Springer

Journal of optimization theory and applications 70 (1991), S. 443-466

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ISSN: 1573-2878

Keywords: Nonlinear optimization ; parametric programming ; stability of solutions ; optimal control

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00941297

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