Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1142523 | Operations Research Letters | 2014 | 7 Pages |
Abstract
We show that the Lasserre hierarchy of semidefinite programming (SDP) relaxations with a slightly extended quadratic module for convex polynomial optimization problems always converges asymptotically even in the case of non-compact semi-algebraic feasible sets. We then prove that the positive definiteness of the Hessian of the associated Lagrangian at a saddle-point guarantees the finite convergence of the hierarchy. We do this by establishing a new sum-of-squares polynomial representation of convex polynomials over convex semi-algebraic sets.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
V. Jeyakumar, T.S. Phạm, G. Li,