Solving Global Optimization Problems with Sparse Polynomials and Unbounded Semialgebraic Feasible Sets

@inproceedings{Jeyakumar2014SolvingGO,
  title={Solving Global Optimization Problems with Sparse Polynomials and Unbounded Semialgebraic Feasible Sets},
  author={Vaithilingam Jeyakumar and Sun Young Kim and Gyu Myoung Lee and Guxin Li},
  year={2014}
}
We propose a hierarchy of semidenite programming (SDP) relaxations for polynomial optimization with sparse patterns over unbounded feasible sets. The convergence of the proposed SDP hierarchy is established for a class of polynomial optimization problems. This is done by deriving a new sum of squares sparse representation of positivity for a system of coercive polynomials over unbounded semialgebraic sets. We demonstrate that the proposed sparse SDP hierarchy can solve some classes of large… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 25 REFERENCES

Convergent SDP-Relaxations in Polynomial Optimization with Sparsity

  • SIAM Journal on Optimization
  • 2006
VIEW 11 EXCERPTS
HIGHLY INFLUENTIAL

Positive polynomials and sums of squares

VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

Convergence of the Lasserre hierarchy of SDP relaxations for convex polynomial programs without compactness

V. Jeyakumar, G. Li, T. S. Pham
  • Oper. Res. Let.,
  • 2014
VIEW 2 EXCERPTS

Optimality conditions and finite convergence of Lasserre’s

J. Nie
  • hierarchy, Math Program, DOI: DOI 10.1007/s10107-013-0680-x,
  • 2013