# On the Differentiability of the Solution to Convex Optimization Problems

arXiv: https://arxiv.org/abs/1804.05098 · HTML: https://mlsanity.com/paper/1804.05098/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2018.

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## Abstract (arXiv)

In this paper, we provide conditions under which one can take derivatives of the solution to convex optimization problems with respect to problem data. These conditions are (roughly) that Slater's condition holds, the functions involved are twice differentiable, and that a certain Jacobian matrix is non-singular. The derivation involves applying the implicit function theorem to the necessary and sufficient KKT system for optimality.