Optimality conditions and finite convergence of Lasserre’s hierarchy
By Jiawang Nie. Mathematical programming, 2012
296 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/93e08941b426336d31faebae080ae3b4d8db1ed9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Computational Theory and Mathematics
In Numerical Analysis
Citations in the corpus
- Moment/Sum-of-Squares Hierarchy for Complex Polynomial Optimization (2015, methodology): “n the hierarchy includes its comparison with lift-and-project methods [46], a new proof of Putinar’s Positivstellensatz via a 1928 theorem of Po´lya [78], and a proof of generically finite convergence [63]. In 1968, Quillen [73] showed that a real-valued bihomogenous complex polynomial that is positi”