# Quantitative Stability of Variational Systems II. A Framework for Nonlinear Conditioning

@article{Attouch1993QuantitativeSO, title={Quantitative Stability of Variational Systems II. A Framework for Nonlinear Conditioning}, author={H{\'e}dy Attouch and Roger J.-B. Wets}, journal={SIAM J. Optim.}, year={1993}, volume={3}, pages={359-381} }

Stability results of Lipschitz and Holder type are obtained for the solutions and optimal values of optimization problems when perturbations are measured in terms of the $\rho $-epi-distance.

## 95 Citations

### Quantitative stability of variational systems: III.ε-approximate solutions

- MathematicsMath. Program.
- 1993

We prove that theε-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar…

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- 1991

This paper proposes a global measure for the distance between the elements of a variational system (parametrized families of optimization problems).

### Characterizations of Lipschitz Stability in Optimization

- Mathematics
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We show that the following local Lipschitz properties of solutions to generalized equations under canonical perturbations are invariant under smooth approximations: the pseudo-Lipschitz property, the…

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This paper concerns the quantitative stability behavior of optimal solutions to a C 1,1 program depending on a parameter vector. For example, given a strict local minimizer of order 2 which satisfies…

### Solution Sensitivity of Variational Inequalities

- Mathematics
- 1999

Our goal is to show that the continuity of the solutions of monotone variational inequalities with respect to perturbations is independent from the geometrical properties of reflexive Banach spaces.

### Well-Posedness and Optimization under Perturbations

- MathematicsAnn. Oper. Res.
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Estimates of the size of sets of approximate solutions are obtained for well-posed optimization problems in a Banach space, and extended to problems subject to perturbations of a general form. An…

### On weak sharp minima in vector optimization with applications to parametric problems

- Mathematics, Computer Science
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The concepts of weak sharp solutions to vector optimization problems are discussed and as an application the application provides sufficient conditions for stability of solutions in perturbedvector optimization problems.

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We prove a Hölder continuity property of the locally unique solution to a parametric variational inequality without assuming differentiability of the given data.

### Hölder Continuity of a Parametric Generalized Variational Inequality

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- 2014

By using the classic metric projection method, we obtain sufficient conditions for Holder continuity of the nonunique solution mapping for a parametric generalized variational inequality with respect…

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