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# Optimization of Polynomial Functions

Published:2003-12-01
Printed: Dec 2003
• M. Marshall
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## Abstract

This paper develops a refinement of Lasserre's algorithm for optimizing a polynomial on a basic closed semialgebraic set via semidefinite programming and addresses an open question concerning the duality gap. It is shown that, under certain natural stability assumptions, the problem of optimization on a basic closed set reduces to the compact case.
 MSC Classifications: 14P10 - Semialgebraic sets and related spaces 46L05 - General theory of $C^*$-algebras 90C22 - Semidefinite programming

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