We consider the global minimization of a multivariate polynomial on a compact semialgebraic set. Using a result of Krivine [J. Analyse Math., 12 (1964), pp. 307--326; C. R. Acad. Sci. Paris, 258 (1964), pp. 3417--3418], it is shown that LP-relaxations based on products of the original constraints, in the spirit of the reformulation-linearization technique procedure of Sherali and Adams, converge to the global optimum. This extends to compact semialgebraic sets, previous results known for polytopes, and 0-1 programs. The asymptotic behavior of the LP-relaxations is also analyzed, and it is shown that in important cases, finite convergence cannot occur.
No takes yet. Share an insight, caveat, or question.
Jean B. Lasserre (2005) studied this question.
Synapse has enriched 4 closely related papers on similar clinical questions. Consider them for comparative context: