Armand Gissler

École Polytechnique · Centre de Mathématiques Appliquées (CMAP) UMR CNRS 7641

We analyze a stochastic process resulting from the normalization of states in the zeroth-order optimization method CMA-ES. On a specific class of minimization problems where the objective function is scaling-invariant, this process defines a time-homogeneous Markov chain whose convergence at a geometric rate can imply the linear convergence of CMA-...

We study the question as to when the closed convex hull of the graph of a K-convex map equals its K-epigraph. In particular, we shed light onto the smallest cone K such that a given map has convex and closed K-epigraph, respectively. We apply our findings to several examples in matrix space as well as to convex composite functions.

Scaling-invariant functions preserve the order of points when the points are scaled by the same positive scalar (usually with respect to a unique reference point). Composites of strictly monotonic functions with positively homogeneous functions are scaling-invariant with respect to zero. We prove in this paper that also the reverse is true for larg...

We study the question as to when the closed convex hull of a K-convex map equals its K-epigraph. In particular, we shed light onto the smallest cone K such that a given map has convex and closed K-epigraph, respectively. We apply our findings to several examples in matrix space as well as to convex composite functions.

Scaling-invariant functions preserve the order of points when the points are scaled by the same positive scalar (with respect to a unique reference point). Composites of strictly monotonic functions with positively homogeneous functions are scaling-invariant with respect to zero. We prove in this paper that the reverse is true for large classes of...