On the Lasserre Hierarchy of Semidefinite Programming Relaxations of Convex Polynomial Optimization Problems

@article{Klerk2011OnTL,
  title={On the Lasserre Hierarchy of Semidefinite Programming Relaxations of Convex Polynomial Optimization Problems},
  author={Etienne de Klerk and Monique Laurent},
  journal={SIAM Journal on Optimization},
  year={2011},
  volume={21},
  pages={824-832}
}
The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions. [J.B. Lasserre. Convexity in semialgebraic geometry and polynomial optimization. SIAM J. Optim. 19, 1995–2014, 2009.] We give a new proof of the finite convergence property, that does not require the assumption that the Hessian of the objective be positive definite on the entire feasible set, but only at the optimal solution. In… CONTINUE READING
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