### Abstract

Language | English |
---|---|

Publisher | Optimization Online |

State | Published - May 2017 |

### Fingerprint

### Keywords

- Polynomial optimization
- Sparse sum-of-squares hierarchy
- Semi-definite programming
- Pooling problem
- Chordal sparsity structure

### Cite this

*Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy*. Optimization Online.

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**Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy.** / Marandi, Ahmadreza; de Klerk, Etienne; Dahl, Joachim.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

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 - 2017/5

Y1 - 2017/5

N2 - The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven 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.

AB - The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven 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.

KW - Polynomial optimization

KW - Sparse sum-of-squares hierarchy

KW - Semi-definite programming

KW - Pooling problem

KW - Chordal sparsity structure

M3 - Discussion paper

BT - Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy

PB - Optimization Online

ER -