# Newton Polytopes and Relative Entropy Optimization

@article{Murray2018NewtonPA, title={Newton Polytopes and Relative Entropy Optimization}, author={R. Murray and V. Chandrasekaran and A. Wierman}, journal={arXiv: Optimization and Control}, year={2018} }

Newton polytopes play a prominent role in the study of sparse polynomial systems, where they help formalize the idea that the root structure underlying sparse polynomials of possibly high degree ought to still be "simple." In this paper we consider sparse polynomial optimization problems, and we seek a deeper understanding of the role played by Newton polytopes in this context. Our investigation proceeds by reparametrizing polynomials as signomials -- which are linear combinations of… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 63 REFERENCES

The REPOP Toolbox: Tackling Polynomial Optimization Using Relative Entropy Relaxations

- Mathematics
- 2017

6

Lower Bounds for Polynomials with Simplex Newton Polytopes Based on Geometric Programming

- Computer Science, Mathematics
- 2016

12

Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization

- Mathematics
- 2000

1850

Global Optimization of Nonconvex Polynomial Programming Problems Having Rational Exponents

- Mathematics, Computer Science
- 1998

65

DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization

- Mathematics, Computer Science
- 2019

90