Zhou, J.Tits, A.L.This note reviews a few existing methods to maintain the positive definiteness of BFGS in constrained optimization, and their impacts on both global and local convergence. The boundedness of the matrix from above is also briefly addressed. Some new strategies are proposed. Convergence analysis and numerical examples are not included.en-UScomputer aided designconstrained optimizationpositive definitenessBFGS updategloballocal convergenceIntelligent ServomechanismsTechnical Report