Franccois Cl'ement

activity

20242026

collaborators

17 papers

math.OC2026

Gradient descent with exponentially increasing stepsizes and restarts

FranÃ§ois ClÃ©ment, Stefan Steinerberger

Let $f : R^{d} \to R$ . We consider gradient descent $x_{n + 1} = x_{n} - I ¨ _{n} \nabla f (x_{n})$ , where the stepsize $I ¨ _{n} = I ¨ \cdot e^{r n}$ is exponentially growing…

cs.LG2026

An effective variant of the Hartigan $k$ -means algorithm

FranÃ§ois ClÃ©ment, Stefan Steinerberger

The k-means problem is perhaps the classical clustering problem and often synonymous with Lloyd's algorithm (1957). It has become clear that Hartigan's algorithm (1975) gives bette…

cs.LO2026

A Rocq Formalization of Simplicial Lagrange Finite Elements

Sylvie Boldo, FranÃ§ois ClÃ©ment, Vincent Martin +2

Formalization of mathematics is a major topic, that includes in particular numerical analysis, towards proofs of scientific computing programs. The present study is about the finit…

math.CA2025

Many critical points for discrete Riesz energy on $T^{2}$

FranÃ§ois ClÃ©ment, Stefan Steinerberger

It is widely believed that the energy functional $E_{p} : (S^{2})^{n} \to R$ $E_{p} = i \neq = j i , j = 1 \sum n \frac{1}{∥ x _{i} - x _{j} ∥ ^{p}}$ has a number of cr…

cs.LO2025

A Rocq Formalization of Monomial and Graded Orders

Even if binary relations and orders are a common formalization topic, we need to formalize specific orders (namely monomial and graded) in the process of formalizing in Rocq the fi…

math.CO2025

Balanced Stick Breaking

Consider an infinite sequence $(x_{k})_{k = 1}^{\infty}$ on the unit circle $S^{1}$ . We may interpret the first $n$ elements $(x_{k})_{k = 1}^{n}$ as places where the `circular stic…

Gradient descent with exponentially increasing stepsizes and restarts

An effective variant of the Hartigan k-means algorithm

A Rocq Formalization of Simplicial Lagrange Finite Elements

Many critical points for discrete Riesz energy on T2

A Rocq Formalization of Monomial and Graded Orders

Balanced Stick Breaking

An effective variant of the Hartigan $k$ -means algorithm

Many critical points for discrete Riesz energy on $T^{2}$