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## Self-concordance

### Shortcomings of classical convergence analysis
- Depends on unknown constants \((m, L, \ldots)\)
- Bound is not affinely invariant, although Newton’s method is

### Convergence analysis via self-concordance (Nesterov and Nemirovski)
- Does not depend on any unknown constants
- Gives affine-invariant bound
- Applies to special class of convex functions ('self-concordant' functions)
- Developed to analyze polynomial-time interior-point methods for convex optimization

*A. d’Aspremont. Convex Optimization M2.*  
*Slide 26/53*
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