This thesis has two main objectives, namely an attempt to give a thorough presentation of the AVP and its applications in cosmology, and testing different optimizing methods, trying to find the most efficient one. A justification for these choices follows.
The AVP has now been discussed in literature for ten years, but no publication has so far been able to give a detailed and pedagogical presentation of the method. It takes quite an effort to get through all the publications on the subject, which does not necessarily guarantee that one fully understands every aspect of the method. I will therefore try to give a presentation that can be followed by anyone with general knowledge of physics, astrophysics, numerical analysis, and mathematics, hopefully without too much effort. The very elegant and efficient AVP method deserves to reach a wider audience than the occasional professor with a particular interest. In addition, the complete sourcecode for locating the stationary values of the action will, to my knowledge, for the first time be given.
The second main objective is to test several different numerical optimizing methods in an attempt to find the most efficient one. In literature, just two such methods have been applied, in addition to a root finding procedure, indicating that there might be other optimizing methods that could prove to be just as efficient, if not better. In numerical literature, the two optimizing methods previously applied to the AVP is generally accepted to be the ones not to prefer. I will therefore test three additional optimizing methods, resulting in a total of 12 different implementations. A brief presentation of all these numerical methods will be given.
In addition to these two main objectives, some cosmology has also been included. The largest system that the different optimizing methods will be tested on consists of 22 mass tracers in the Local Group and the Local Neighbourhood. The system reach as far as 6-7 Mpc, and will therefore most probably give a relatively poor fit with observations. I will then try to adjust the input distance to some of the mass tracers in an attempt to get a better agreement between observed and predicted values of the radial velocities. This will give an indication of the preferred distance of these mass tracers based on the AVP. It should also be noted that the system of mass tracers here has been extended by a couple of newly discovered galaxies in the Local Neighbourhood.