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2014

Strong duality in Lasserre's hierarchy for polynomial optimization

Josz, Cédric, Henrion, Didier

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A polynomial optimization problem (POP) consists of minimizing a multivariate real polynomial on a semi-algebraic set $K$ described by polynomial inequalities and equations.

In its full generality it is a non-convex, multi-extremal, difficult global optimization problem.
More than an decade ago, J.~B.~Lasserre proposed to solve POPs by a hierarchy of convex semidefinite programming (SDP) relaxations of increasing size.
Each problem in the hierarchy has a primal SDP formulation (a relaxation of a moment problem) and a dual SDP formulation (a sum-of-squares representation of a polynomial Lagrangian of the POP).

Strong duality in Lasserre's hierarchy for polynomial optimization · Around

Built on

Optimisation globale et théorie des moments
J. B. Lasserre · 2000
Earlier work this paper cites.
Duality, optimality conditions and perturbation analysis
A. Shapiro · 2000
Earlier work this paper cites.
Global optimization with polynomials and the problem of moments
J. B. Lasserre · 2001
Earlier work this paper cites.

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Then

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Optimality conditions and finite convergence of Lasserre’s hierarchy
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