In the first part of this report, I will talk about the relationship between the existence of twisted K/"ahler-Ricci  solitons and the properness of modified twisted $K$-energy. In the second part, we consider the conical K/"ahler-Ricci solitons on Fano manifold. Approximating by a sequence of smooth twisted K/"ahler-Ricci solitons, we obtain an existence result of conical K/"ahler-Ricci solitons.

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