Stephanie Caro | Searcharxiv

arXiv2026

Explicit data-dependent characterizations of the subdifferential of convex pointwise suprema and optimality conditions

We establish explicit data-dependent and symmetric characterizations of the subdifferential of the supremum of convex functions, formulated directly in terms of the underlying data functions. In our approach, both active and non-active functions contribute equally through their subdifferentials, thereby avoiding the need for additional geometric constructions, such as the domain of the supremum, that arise in previous developments. Applications to infinite convex optimization yield sharp Karush-Kuhn-Tucker and Fritz-John optimality conditions, expressed exclusively in terms of the objective and constraint functions and clearly distinguishing the roles of (almost) active and non-active constraints.

math.OC↗

arXiv2026

Normal cones to sublevel sets of convex and quasi-convex supremum functions

We provide sharp and explicit characterizations of the normal cone to sublevel sets of suprema of arbitrary functions, expressed exclusively in terms of subdifferentials of the data functions. In the convex case, the resulting formulas involve the approximate subdifferential of the individual data functions at the nominal point. In contrast, the quasi-convex framework requires the use of the Fr\'echet subdifferential of these data functions but evaluated at nearby points. These results are applied to derive optimality conditions for infinite convex and quasi-convex optimization problems.

math.OC↗