### Abstract

Original language | English |
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Journal | Discrete Applied Mathematics |

DOIs | |

Publication status | E-pub ahead of print - 2018 |

### Fingerprint

### Keywords

- polynomial optimization
- sparse sum-of-squares hierarchy
- semi-definite programming
- pooling problem
- chordal sparsity structure
- discrete-time optimal control

### Cite this

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**Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy.** / de Klerk, Etienne; Marandi, Ahmadreza; Dahl, Joachim.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy

AU - de Klerk, Etienne

AU - Marandi, Ahmadreza

AU - Dahl, Joachim

PY - 2018

Y1 - 2018

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 - polynomial optimization

KW - sparse sum-of-squares hierarchy

KW - semi-definite programming

KW - pooling problem

KW - chordal sparsity structure

KW - discrete-time optimal control

U2 - 10.1016/j.dam.2017.12.015

DO - 10.1016/j.dam.2017.12.015

M3 - Article

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -