Symmetry Reduction in AM/GM-Based Optimization - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Optimization Année : 2022

Symmetry Reduction in AM/GM-Based Optimization

Résumé

The arithmetic mean/geometric mean inequality (AM/GM inequality) facilitates classes of nonnegativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic study of the AM/GM-based techniques in the presence of symmetries under the linear action of a finite group. We prove a symmetry-adapted representation theorem and develop techniques to reduce the size of the resulting relative entropy programs. We study in more detail the complexity gain in the case of the symmetric group. In this setup, we can show in particular certain stabilization results. We exhibit several sequences of examples in growing dimensions where the size of the reduced problem stabilizes. Finally, we provide some numerical results, emphasizing the computational speedup.

Dates et versions

hal-03924189 , version 1 (05-01-2023)

Identifiants

Citer

Philippe Moustrou, Helen Naumann, Cordian Riener, Thorsten Theobald, Hugues Verdure. Symmetry Reduction in AM/GM-Based Optimization. SIAM Journal on Optimization, 2022, 32 (2), pp.765-785. ⟨10.1137/21M1405691⟩. ⟨hal-03924189⟩
24 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More