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Symmetry Reduction in AM/GM-Based Optimization

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.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.32 No.2 April-June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 765-785

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

POSITIVE FUNCTIONS
SAGE CERTIFICATES
SYMMETRY REDUCTION
RELATIVE ENTROPY PROGRAMMING

Info Detail Spesifik

https://doi.org/10.1137/21M1405691

Pernyataan Tanggungjawab

Philippe Moustrou, Helen Naumann, Cordian Riener, Thorsten Theobald, Hugues Verdure

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