Optimality conditions and finite convergence of Lasserre’s hierarchy View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2014-08

AUTHORS

Jiawang Nie

ABSTRACT

Lasserre’s hierarchy is a sequence of semidefinite relaxations for solving polynomial optimization problems globally. This paper studies the relationship between optimality conditions in nonlinear programming theory and finite convergence of Lasserre’s hierarchy. Our main results are: (i) Lasserre’s hierarchy has finite convergence when the constraint qualification, strict complementarity and second order sufficiency conditions hold at every global minimizer, under the standard archimedean condition; the proof uses a result of Marshall on boundary hessian conditions. (ii) These optimality conditions are all satisfied at every local minimizer if a finite set of polynomials, which are in the coefficients of input polynomials, do not vanish at the input data (i.e., they hold in a Zariski open set). This implies that, under archimedeanness, Lasserre’s hierarchy has finite convergence generically. More... »

PAGES

97-121

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10107-013-0680-x

DOI

http://dx.doi.org/10.1007/s10107-013-0680-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1029482687


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