Applying Lasserre hierarchy for solving polynomial feasible problems
Tutor / director / evaluatorEisenbrand, Friedrich; Heredia, F.-Javier (Francisco Javier); Malinović, Igor
Document typeBachelor thesis
Rights accessRestricted access - confidentiality agreement
Solving feasibility for polynomial problems is NP-hard in general, and actual softwares have a double exponential computational time. In this report, a Positive semidefinite relaxation of the problem that we call the Generalized Lasserre Hierarchy will be proposed, this relaxation appears to be solved faster than the original problem. It involves positive semidefinite moment matrices and moment matrices of slacks. We will introduce it and present some theoretical background that includes theory in the field of semidefinite duality and sum of squares in order to study its complexity and asymptotic convergence. Asymptotic evolution will be also studied both theoretically and via experimentation. Eventually, in the conclusion we expose future directions in order to improve this relaxation.
Discrete Optimization Group (EPFL)