## Exact Conic Programming Relaxations for a Class of Convex Polynomial Cone Programs

- Vaithilingam Jeyakumar, Guoyin Li
- J. Optimization Theory and Applications
- 2017

1 Excerpt

- Published 2016 in SIAM Journal on Optimization

In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming (SDP) relaxations and provide convergence results for the methods. Our scheme for problems with a convex lower-level problem involves solving a transformed equivalent single-level problem by a sequence of SDP relaxations; whereas our approach for general problems involving a non-convex polynomial lower-level problem solves a sequence of approximation problems via another sequence of SDP relaxations.

@article{Jeyakumar2016ConvergentSP,
title={Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems},
author={Vaithilingam Jeyakumar and Jean B. Lasserre and Guoyin Li and T. S. Pham},
journal={SIAM Journal on Optimization},
year={2016},
volume={26},
pages={753-780}
}