The paper studies the partial infimal convolution of the generalized matrix-fractional function with a closed, proper, convex function on the space of real symmetric matrices. Particular attention is given to support functions and convex indicator functions. It is shown that this process yields approximate smoothings of all Ky-Fan norms, weighted nuclear norms, and much more. In particular, it is proven that all variational Gram functions are the square of a weighted gauge. A complete variational calculus is given for this class of functions including formulas for their conjugates and subdifferentials. 查看全文>>