By measuring and adjusting the beta-functions at the interaction point (IP the luminosity is being optimized. In LEP (Large Electron Positron Collider) this was done with the two closest doublet magnets. This approach is not applicable for the LHC (Large Hadron Collider) and RHIC (Relativistic Heavy Ion Collider) due to the asymmetric lattice. In addition in the LHC both beams share a common beam pipe through the inner triplet magnets (in these region changes of the magnetic field act on both beams). To control and adjust the beta-functions without perturbation of other optics functions, quadrupole groups situated on both sides further away from the IP have to be used where the two beams are already separated. The quadrupoles are excited in specific linear combinations, forming the so-called "tuning knobs" for the IP beta-functions. For a specific correction one of these knobs is scaled by a common multiplier. The different methods which were used to compute such knobs are discussed: (1) matching in MAD, (2)inversion and conditioning of the response matrix by singular value decomposition, and (3)conditioning the response matrix by multidimensional minimization using an adapted Moore Penrose method. For each accelerator, LHC and RHIC, a set of knobs was calculated and the performance compared. In addition the knobs for RHIC were successfully applied to the accelerator. Simultaneously this approach allows us theoretically to measure the beam sizes of both colliding beams at the IP, based on the tuneability provided by the knobs. This possibility was investigated. The standard method for LEP to measure the IP beta-functions was adapted and advanced to the asymmetric LHC lattice
