863 citations
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- Centre National de la Recherche ScientifiqueFR339 papers
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5 papers · 2 filters
Lebesgue decomposition in action via semidefinite relaxations
Jean-Bernard Lasserre
Given all (finite) moments of two measures and on , we provide a numerical scheme to obtain the Lebesgue decomposition with and . When has…
Moments and Legendre-Fourier Series for Measures Supported on Curves
Jean B. Lasserre
Some important problems (e.g., in optimal transport and optimal control) have a relaxed (or weak) formulation in a space of appropriate measures whichis much easier to solve. Howev…
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…
A max-cut formulation of 0/1 programs
Jean-Bernard Lasserre
We show that the linear or quadratic 0/1 program\[P:\quad\min\{ c^Tx+x^TFx : \:A\,x =b;\:x\in\{0,1\}^n\},\]can be formulated as a MAX-CUT problem whose associated graph is simply r…
A bounded degree SOS hierarchy for polynomial optimization
Jean-Bernard Lasserre, Toh Kim-Chuan, Yang Shouguang
We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem on a compact basic semi-algebraic…