TY - JOUR
T1 - Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy
AU - Marandi, Ahmadreza
AU - de Klerk, Etienne
AU - Dahl, Joachim
PY - 2020
Y1 - 2020
N2 - The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem, as well as a discrete-time optimal control problem.
AB - The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser et al. (2017) constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proved by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality constraints directly, without eliminating or replacing them by two inequalities. We also evaluate the sparse-BSOS hierarchy on a well-known bilinear programming problem, called the pooling problem, as well as a discrete-time optimal control problem.
KW - Chordal sparsity structure
KW - Discrete-time optimal control
KW - Polynomial optimization
KW - Pooling problem
KW - Semi-definite programming
KW - Sparse sum-of-squares hierarchy
UR - http://www.scopus.com/inward/record.url?scp=85039960090&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2017.12.015
DO - 10.1016/j.dam.2017.12.015
M3 - Article
AN - SCOPUS:85039960090
SN - 0166-218X
VL - 275
SP - 95
EP - 110
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -