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Author

F. M. Pirani

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3 papers indexed here

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Preprint Sep 2026

DC decompositions and cutting-plane approximation: geometry and complexity

We study how Difference of Convex (DC) decomposition affects cutting-plane approximation in global optimization. For a smooth decomposition $f = g-h$, let $d$ be the dimension of the span of all Hessian ranges of $g$ over the convex hull of a compact feasible set. The smallest attainable dimension equals the minimum ra...

F. M. Pirani · 0 citations
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

In the nonconvex case, it is proved that quadratic growth in conjunction with a regularity property for the active gradients suffices, and it is proved that quadratic growth in conjunction with a regularity property for the active gradients suffices.

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

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