The layout of the paper is as follows. In Section \[antares\], the main features of the ANTARES neutrino telescope and the reconstruction algorithms used in this work are explained. In Section \[simulation\], the expected signal from WIMP self-annihilation from the GC, and the background expected from atmospheric muons and neutrinos are reported. In Section \[optimisation\], the method used to optimise the selection of the neutrino events is described. Finally, the results obtained are discussed in Section \[results\], where limits on the neutrino plus anti-neutrino flux $\rm \Phi_{\nu_{\mu}+\bar{\nu}_\mu}$ are derived from the absence of a signal. The corresponding 90% C.L. upper limits on the velocity-averaged annihilation cross-section $\rm <\sigma_{A}v>$ are obtained for different benchmark channels of self-annihilation, and compared to the latest constraints from other experiments. In the following, neutrino will mean neutrino plus anti-neutrino, unless explicitly stated otherwise.

The ANTARES Neutrino Telescope {#antares}
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ANTARES is the first undersea neutrino telescope and the largest of its kind in the Northern Hemisphere [@antares]. It is located at 2475 m below the Mediterranean Sea level, $40$ km offshore from Toulon (France) at $42^{\circ} 48$’ N and $6^{\circ} 10$’ E. The telescope consists of $12$ detection lines with 25 storeys each. A standard 