Semidefinite programming

Adjacency list

Monomial

Algorithm

Discrete mathematics

Physics

Mathematical optimization

Diagonal

Mathematical analysis

Economics

Exploit

Moment (physics)

Geometry

Hierarchy

Mathematics

Market economy

Computer security

Computer science

Term (time)

Quantum mechanics

Classical mechanics

Polynomial

SIAM Journal on Optimization

This paper is concerned with polynomial optimization problems. We show how to exploit term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of semidefinite programming relaxations. The novelty (and distinguishing feature) of such relaxations is to involve block-diagonal matrices obtained in an iterative procedure performing completion of the connected components of certain adjacency graphs. The graphs are related to the terms arising in the original data and not to the links between variables. Our theoretical framework is then applied to compute lower bounds for polynomial optimization problems either randomly generated or coming from the networked system literature.

TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity