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This paper proposes a new design methodology of arbitrarily shaped integrated lens antennas (ILAs). First, we describe the design principles and numerical techniques of the optimization iterative loop. The starting lens shape, deduced from a general synthesis method based on geometrical optics principles, is optimized so that the radiation pattern of the ILA complies with an arbitrary amplitude-shaped template. The optimization procedure is local and is based on a multidimensional conjugate gradient method. Then, the capabilities and potentialities of this approach are demonstrated numerically using two examples. In the first one, an ILA radiating a secant-squared beam in one principal plane and a flat-top beam in the orthogonal plane is designed for indoor communications in V-band. In the second example (Gaussian/flat-top beam), we show for the first time that the joint optimization of the feed together with the lens shape is a very promising design methodology. Finally, our design tools are validated experimentally in Q-band through the synthesis and optimization of a peculiar small shaped ILA (28 mm×28 mm×15 mm) fed by an aperture-coupled microstrip patch antenna.