42 citations · 66 across the 12 of their papers we have counts for
13 papers
Convergence rates of RLT and Lasserre-type hierarchies for the generalized moment problem over the simplex and the sphere
Felix Kirschner, Etienne de Klerk
We consider the generalized moment problem (GMP) over the simplex and the sphere. This is a rich setting and it contains NP-hard problems as special cases, like constructing optima…
An Analytic Center Cutting Plane Method to Determine Complete Positivity of a Matrix
Riley Badenbroek, Etienne de Klerk
We propose an analytic center cutting plane method to determine if a matrix is completely positive, and return a cut that separates it from the completely positive cone if not. Thi…
Minimum energy configurations on a toric lattice as a quadratic assignment problem
Daniel Brosch, Etienne de Klerk
We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex quadratic programming (CQP), and a semidefinite programming (SDP) bound. Since th…
Simulated annealing with hit-and-run for convex optimization: rigorous complexity analysis and practical perspectives for copositive programming
Riley Badenbroek, Etienne de Klerk
We give a rigorous complexity analysis of the simulated annealing algorithm by Kalai and Vempala [Math of OR 31.2 (2006): 253-266] using the type of temperature update suggested by…
Complexity Analysis of a Sampling-Based Interior Point Method for Convex Optimization
Riley Badenbroek, Etienne de Klerk
We develop a short-step interior point method to optimize a linear function over a convex body assuming that one only knows a membership oracle for this body. The approach is based…
Worst-case examples for Lasserre's measure--based hierarchy for polynomial optimization on the hypercube
Etienne de Klerk, Monique Laurent
We study the convergence rate of a hierarchy of upper bounds for polynomial optimization problems, proposed by Lasserre [SIAM J. Optim. 21(3) (2011), pp. 864-885], and a related hi…