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Context. Since 1995 and the first discovery of an exoplanet orbiting a main-sequence star, 4000 exoplanets have been discovered using several techniques. However, only a few of these exoplanets were detected through direct imaging. Indeed, the imaging of circumstellar environments requires high-contrast imaging facilities and accurate control of wavefront aberrations. Ground-based planet imagers such as VLT/SPHERE or Gemini/GPI have already demonstrated great performance. However, their limit of detection is hampered by suboptimal correction of aberrations unseen by adaptive optics (AO). Aims. Instead of focusing on the phase minimization of the pupil plane as in standard AO, we aim to directly minimize the stellar residual light in the SPHERE science camera behind the coronagraph to improve the contrast as close as possible to the inner working angle. Methods. We propose a dark hole (DH) strategy optimized for SPHERE. We used a numerical simulation to predict the global improvement of such a strategy on the overall performance of the instrument for different AO capabilities and particularly in the context of a SPHERE upgrade. Then, we tested our algorithm on the internal source with the AO in closed loop. Results. We demonstrate that our DH strategy can correct for aberrations of phase and amplitude. Moreover, this approach has the ability to strongly reduce the diffraction pattern induced by the telescope pupil and the coronagraph, unlike methods operating at the pupil plane. Our strategy enables us to reach a contrast of 5e-7 at 150 mas from the optical axis in a few minutes using the SPHERE internal source. This experiment establishes the grounds for implementing the algorithm on sky in the near future.