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Zbl 0915.49021
Bonnans, J.Frédéric; Shapiro, Alexander
Optimization problems with perturbations: A guided tour.
(English)
[J] SIAM Rev. 40, No.2, 228-264 (1998). ISSN 0036-1445; ISSN 1095-7200/e

The authors present an overview of some recent progress in the theory of optimization problems with perturbations of the form $$\underset{x\in X}\to{\text{Minimum}} f(x,u),\qquad \text{subject to }x\ (u),$$ where $X$ is a Banach space and the perturbation parameter $u$ can be a scalar, a finite-dimensional vector or an element of a metric space $U$.\par Mainly, methods based on upper and lower estimates of the objective function of the perturbed problem are considered. Some illustrations are given by computing the equilibrium position of a chain that is almost vertical or horizontal.
[H.Benker (Merseburg)]
MSC 2000:
*49K27 Optimal control problems in abstract spaces (nec./ suff.)
49K40 Sensitivity of optimal solutions in the presence of perturbations
90C31 Sensitivity, etc.
65K05 Mathematical programming (numerical methods)
90C48 Programming in abstract spaces
49J52 Nonsmooth analysis (other weak concepts of optimality)

Keywords: sensitivity analysis; parameterized optimization; directional differentiability; quantitative stability; duality; expansion of optimal solutions; semi-infinite programming; semidefinite programming; second-order optimality conditions

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