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Convex Optimization by Lieven Vandenberghe, Stephen Boyd

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5.6 Perturbation and sensitivity analysis

When strong duality obtains, the optimal dual variables give very useful information about the sensitivity of the optimal value with respect to perturbations of the constraints.

5.6.1 The perturbed problem

We consider the following perturbed version of the original optimization problem (5.1):

image

(5.56)

with variable x Rn. This problem coincides with the original problem (5.1) when u = 0, υ = 0. When ui is positive it means that we have relaxed the ith inequality constraint; when ui is negative, ...

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