Relaxation in infinite convex programming under Slater-type regularity conditions
Optimization and Control
2026-02-06 v1 Functional Analysis
Abstract
The main purpose of this paper is to close the gap between the optimal values of an infinite convex program and that of its biconjugate relaxation. It is shown that Slater and continuity-type conditions guarantee such a zero-duality gap. The approach uses calculus rules for the conjugation and biconjugation of the sum and pointwise supremum operations. A second important objective of this work is to exploit these results on relaxation by applying them in the context of duality theory.
Cite
@article{arxiv.2602.05457,
title = {Relaxation in infinite convex programming under Slater-type regularity conditions},
author = {Rafael Correa and Abderrahim Hantoute and Marco A. López},
journal= {arXiv preprint arXiv:2602.05457},
year = {2026}
}