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The adjoint method is an efficient technique for the topology optimization of complex nanophotonic systems, including nanostructures, metasurfaces and integrated optical circuits. While such method has been traditionally used in the frequency domain, its extension to the time domain opens new opportunities for wideband optimization of dispersive materials for applications ranging from broadband absorbers to enhanced quantum emitters in dispersive environments. We propose a topology optimization technique for the inverse design of linear optical materials with arbitrary dispersion and anisotropy. We introduce a general adjoint scheme in the time-domain based on the complex-conjugate pole-residue pair (CCPR) model. This approach has the advantage of treating dispersive media and broadband response naturally in a single simulation run. We implement this framework within the finite-difference time-domain (FDTD) method and investigate the method for optimizing metallic and dielectric nanoantennas over the optical spectral range of 350-1000 nm. The combination of the method with parallel computing enables the large-scale inverse design of nanostructures in 3D with extreme field confinement. Nanostructures found via inverse design and featuring the intriguing anapole effect are also discussed. This effect enables nanostructures that show field enhancement, negligible scattering, and low losses. The possibility of reducing losses in plasmonic nanostructures via inverse design is an interesting possibility offered by the method and may open new avenues towards the realization of transparent plasmonic metamaterials for applications in linear and nonlinear nanophotonics.