3 citations · 4 across the 4 of their papers we have counts for
7 papers
On the convergence rate of grid search for polynomial optimization over the simplex
Etienne de Klerk, Monique Laurent, Zhao Sun +1
We consider the approximate minimization of a given polynomial on the standard simplex, obtained by taking the minimum value over all rational grid points with given denominator ${…
Bound-constrained polynomial optimization using only elementary calculations
Etienne de Klerk, Jean Lasserre, Monique Laurent +1
We provide a monotone non increasing sequence of upper bounds () converging to the global minimum of a polynomial on simple sets like the unit hypercube. The no…
Convergence analysis for Lasserre's measure--based hierarchy of upper bounds for polynomial optimization
Etienne de Klerk, Monique Laurent, Zhao Sun
We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp.…
An error analysis for polynomial optimization over the simplex based on the multivariate hypergeometric distribution
Etienne de Klerk, Monique Laurent, Zhao Sun
We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a…
A refined error analysis for fixed-degree polynomial optimization over the simplex
Zhao Sun
We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set proble…
An alternative proof of a PTAS for fixed-degree polynomial optimization over the simplex
Etienne de Klerk, Monique Laurent, Zhao Sun
The problem of minimizing a polynomial over the standard simplex is one of the basic NP-hard nonlinear optimization problems --- it contains the maximum clique problem in graphs as…