Author

F. M. Pirani

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Preprint Sep 2026

Effective curvature dimension in smooth DC optimization

We introduce the effective curvature dimension of a smooth DC decomposition, defined as the dimension of the span of the Hessian ranges of its first convex component. We prove that the smallest attainable effective dimension over all smooth DC decompositions equals the minimum rank of a positive semidefinite matrix tha...

F. M. Pirani · 0 citations

Preprint Aug 2026

Strong growth and Goldstein subgradients in piecewise smooth optimization

We explore a new growth condition for Lipschitz functions around local minimizers, recently proposed in the context of Goldstein-subgradient-based algorithms and their behavior in practice. On generic examples, these algorithms are often observed to converge approximately linearly. We focus on objectives that are piece...

Adrian S. Lewis, F. M. Pirani · 0 citations