The central region of the dark matter halo of the Milky Way is a promising target for a search for a particle dark matter annihilation signal. The H.E.S.S. Collaboration has published a search for a photon flux originating from dark matter particles annihilating in the galactic center region. No significant excess was observed and upper limits on the velocity averaged dark matter self annihilation cross section were derived. The limits exclude the self annihilation of dark matter particles in the $\sim 1$ TeV to $\sim 4$ TeV mass range with a velocity averaged annihilation cross section larger than $\sim 3\cdot 10^{-25}\:\mathrm{cm^3/s}$, i.e. about one order of magnitude above the prediction for a thermal relic dark matter particle. A detailed and realistic Monte Carlo study of new strategies for the search for a particle dark matter annihilation signal from the Milky Way dark matter halo with the High Energy Stereoscopic System is presented and the sensitivity of different experimental approaches is compared.