We first describe a method, based on the simulated annealing approach, for determining a modern energy density functional within the Skyrme Hartree-Fock (HF) theory by carrying out a fit to extensive set of experimental data with additional constraints on the Skyrme parameters. Next, we review the HF-based random phase approximation (RPA) approach for calculating properties of giant resonances. We then present results of calculations for the centroid energies of giant resonances within the HF-based RPA and discuss the current status of the equation of state of nuclear matter.

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