# Exact SDP relaxations of quadratically constrained quadratic programs with forest structures

@inproceedings{Azuma2020ExactSR, title={Exact SDP relaxations of quadratically constrained quadratic programs with forest structures}, author={Godai Azuma and M. Fukuda and Sunyoung Kim and M. Yamashita}, year={2020} }

We study the exactness of the semidefinite programming (SDP) relaxation of quadratically constrained quadratic programs (QCQPs). With the aggregate sparsity matrix from the data matrices of a QCQP with n variables, the rank and positive semidefiniteness of the matrix are examined. We prove that if the rank of the aggregate sparsity matrix is not less than n − 1 and the matrix remains positive semidefinite after replacing some off-diagonal nonzero elements with zeros, then the standard SDP… CONTINUE READING

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 34 REFERENCES

Exploiting Aggregate Sparsity in Second Order Cone Relaxations for Quadratic Constrained Quadratic Programming Problems

- Mathematics
- 2019

1

Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations

- Mathematics, Computer Science
- 2003

142

Exact semidefinite formulations for a class of (random and non-random) nonconvex quadratic programs

- Computer Science, Mathematics
- 2020

11

Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons

- Mathematics, Computer Science
- 2011

96

On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues

- Mathematics, Computer Science
- 1998

319

BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems with Binary, Box and Complementarity Constraints

- Mathematics
- 2018

3

Finding Low-rank Solutions of Sparse Linear Matrix Inequalities using Convex Optimization

- Computer Science, Mathematics
- 2017

34

Exactness of Semidefinite Relaxations for Nonlinear Optimization Problems with Underlying Graph Structure

- Mathematics, Computer Science
- 2014

64