2021/01/25 by Julio Backhoff‐Veraguas, Backhoff-Veraguas, Julio, Mathias Beiglböck +3
Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Graph theory and applications #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2101.09975
openalex publication_date 2021/01/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other fields where infinite dimensional linear optimization problems play an important role. In this note, we observe how this approach can be transferred to non-linear optimization problems. Specifically we establish a monotonicity principle that is applicable to the Schrödinger problem and use it to characterize the structure of optimizers for target functionals beyond relative entropy. In contrast to classical convex duality approaches, a main novelty is that the monotonicity principle allows to deal also with non-convex functionals.